Britain loaned money to the South (Which has never been paid back), provided them guns, ships and other supplies. Even built ships for the South (or had them converted from existing ships).
The main reason for no intervention was three fold, first internal British opposition to going to war to preserve slavery, Britain had technically abolished Slavery in its colonies in the 1840s do to internal opposition to the institution of Slavery (And no major opposition to such abolishment given that the main source of Cotton for English mills was in the American South, which would be unaffected by the British abolishment of Slavery).
The Second was military, basically by 1862 the two largest Armies in the World were facing each other in Virginia. The British army would NOT provide much support for the South, and the North still had the capability to field an additional Army (The North by 1862 had three Armies in the Field, The Army of the Potomac outside Washington DC, The Army of the Tennessee outside Nashville, the the Army of the Ohio outside St Louis (At Shiloh the Army of Tennessee and Army of the Ohio would be merged, which was the reason Grant was attacked at Shiloh, to prevent that merger of those two armies). Additional substantial forces were in New Orleans. All of this a YEAR BEFORE the draft was instituted in 1863. The North would have various other armies during the war and the names would change over time (The exception was the Army of the Potomac and the Army of the Tennessee, names and Armies that would last to the end of the war). My point is simple, the North could field even more men then it did in 1865 (The US had a million men at arms in 1865, excluding the Militia, which still existed). These could all be set to attack Canada without affecting the north's war against the Confederacy.
Given this HUGE force WITHOUT a draft (and when the Draft was passed it had so many exceptions, including the right to buy your way out of it, it did NOT bring in many new recruits, but did bring in bonus money for any Soldier who wanted to re-enlist but refused do to the lack of enlistment bonuses like the ones that had been popular in 1861). Furthermore, more Canadians were serving in the Union Army then in the Canadian Militia. Now the numbers depends on who is doing the counting, The Union numbers seems to be accurate, through Canadians object to the fact the US Statistics gives an exact number rather than round numbers (British War Gamers of today go with the Union numbers as more accurate, those guys really get into not only the tactics of the armies they are gaming, but how they are formed, by who and why). Canadians tend to use 1861 militia numbers NOT the Militia numbers after the militia reforms of 1862 and 1864 (The reform reflected the fact that a huge number of Canadians did NOT want to fight or otherwise resist an invasion by the US, thus the Canadian Militia was reformed twice during the US Civil War, to make sure it included more and more Canadians who would oppose a US Invasion). Thus given the attitude of many Canadians (Maybe the majority or maybe not the majority, no Canadian Government official did a survey or an election, for fear of the results), and the ability of the US to call even more soldiers into the Union Army, there was no way Britain could hold on to Canada if the US invaded.
Furthermore, the huge introduction of Monitors into the Union Navy gave the US Naval superiority off the US Coast. These ships were NOT design for actions deep into the Atlantic, but it was the British who had to cross the Atlantic and then fight to land and support the South. The Monitors where cheap and quick to built compared to the British Battleships of the time period. Each British Battleship could easily defeat a Monitor, but the prospect was 3-4 monitors on each British Battleship, and in such a case the Battleship would lose. Britain faced not only losing Canada, but some people think they would have had a hard time to hold onto Newfoundland. Nova Scotia and New Brunswick would have quickly fallen to a US Navy Monitor invasion, but Newfoundland is a little to far away for a Monitor to reach and be combat ready (A Monitor did reach England after the war, and the condition of the Ship and crew was horrible according to British reports, but it was more a attempt to show the British that the Monitor was a worthy ship for what it was designed, off the coast of the US, then to show that the US Monitor could attack Britain).
Thus all told, Britain had GOOD military reasons to avoid a war with the US. Memories of the Crimea War was still fresh in the minds of many in Britain. Britain and France won that war, but the problem of Supply had been hopelessly underestimated at the start of the War, and stayed a problem till the end. Going across the Atlantic would require ships capable of traveling the North Atlantic, not the Ships built to help move supplies across the Mediterranean and Black seas. This supply problem added to the Military problems. All together, given the problems, Britain was looking as serious Military losses in any intervention.
The third problem (If the above was not enough), was other commitments. France and Britain had intervene into Mexico in 1862 over economic problems of Mexico, Britain quickly pulled out, but France kept throwing in men and material to defeat the opposition to the Government their imposed. This tied up the France Army and Navy, until France decided to pull out in 1865 (Do to massive amount of Civil War Surplus being sent over the Mexican Border by the US when the Civil War ended AND the Marshaling of potential invasion armies in late 1865 along the same border). Do to the pull out of the French army in 1865, the Mexican government imposed by the France was overthrown in 1867. My point is FRANCE was hopelessly tied up in Mexico to give any assistance to Britain when in came to intervening in the US Civil war. Britain was looking at intervening all by itself.
This was complicated by the Russians. Britain and France had fought the Russians in the Crimea War of 1854. The US had supplied the Russian armies by smuggling supplies through the waters controlled by France, Britain and their ally Turkey into Sevastopol (In fact both McClellan and Stuart of later US Civil War frame saw the Charge of the Light Brigade from the RUSSIAN lines do to how close the US and the Russians were at that time). Russia even sent its fleet to various US Ports during 1862, to show support for the North (This was to be paid by the North, but was NOT done till Alaska was purchased in 1867, the price of the visit was added to the price of Alaska. Furthermore Alaska was "sold" to the US more do to the fact Russia believe the US could defend it better from a British attack then any other reason).
No formal alliance existed between the US and Russian in 1840-1918 period, but both countries had reasons for support each other given that both countries had ongoing conflicts with Britain (The Japanese took the view that the US IMPOSED a Settlement of the Russo- Japanese war of 1905 on the Japanese do to this long term "understanding" and several survivals of the Japanese Defeat of the Russian Fleet escaped to US held Philippines, based on that same long term understanding).
The Russians did NOT have to send troops or ships the US to support the US, all it had to do was stir up the tribes in Afghanistan which would lead to problems in the Indus River Valley of then British Indian (Now Pakistan). This would have required additional British Troops AND ships to get them to India, thus denying any ability of Britain to support the South (Russian seems to have done SOME actions to stir up people in Afghanistan, enough to get the British Attention then anything else).
My point is simple, Britain had several good reason NOT to intervene in the US Civil War even through they were dependent on Southern Cotton. Lincoln played to all of the Reasons Britain should NOT intervene. Lincoln had the Russian Fleet visit the US at the same time he issued the Emancipation Proclamation (Which was more for British consumption then US consumption, Black slave could NOT read and the Conditions in the south, i.e vast new troops all over the place, during the Civil War had made any escape of Slaves almost impossible by 1862 let alone 1863 when the Proclamation kicked in). When a US ships captured two Confederate Ambassadors on a British ship on the High Sea, Lincoln put them back onto a British ship, and paid for the damage to the British ship. Again to provide support for the Anti-intervention forces in Britain, when it was needed. Most British Newspapers in 1862 demanded war over that attack on a British Ship, as an act of war. War seemed on it sway, when News of Lincoln's action was received and used by opponents of going to war to show the US will obey international Law as it fights the South.
Thus Britain did have a dog in the US Civil War (US would sell captured Cotton to Britain all through the War), but do to the above three reasons Britain stayed out of the war for intervention looked like it would be costly.
More on the CSS Shenandoah, the last Confederate Ship to Surrender, NEVER landed anywhere in the NEW World let alone any Port of North America:
http://en.wikipedia.org/wiki/CSS_Shenandoahhttp://www.csa-dixie.com/liverpool_dixie/shenandoah.htm