Wood frigates can't take on the Monitor. Nelson's ship-of-the line HMS Victory can't take on the Monitor.
Victory was a mid 18th century ship, unpowered, and mounted a mix of 32 pounders, 24 pounders, 12 pounders and 68 pounders.
She couldn't take on the Monitor very well.
The actual fleet of the Royal Navy in the 1860s contained some much more formidable wooden frigates - all powered. To pick a name at random from the list of frigates already in North America in 1862, we have the
Immortalite - a 51 gun frigate with a trials speed of 12.3 knots under steam alone, and armed with 15 8" guns and 10 32-pounders each broadside along with one 68 pounder pivot.
The 68 pounder is nearly powerful enough to penetrate the Monitor at close range. The other guns aren't, but they can each be fired at least once per minute - producing a hail of shot which can damage the
Monitor through sheer attrition (in the same way that the monitors attacking Charleston were damaged and disabled) or by hitting her vulnerable gun ports when she turns to fire. If all else fails she can simply ram, as she's three times the mass of the
Monitor and has much more reserve bouyancy.
The ships of the line are much more fearsome. The
Nile (again, North America at the time) had 78 guns in 1862 of which sixteen were rifles, and was a little slower at 8.2 knots; the
Donegal was at Bermuda in 1862 and had a top speed under steam alone of twelve knots (pause for a moment and consider which USN vessels could outspeed her!) with 101 guns, and a designed broadside of 18 8" guns plus 32 32-pounder guns (and a 68 pounder pivot).
For inshore work, there's HMS
Terror - again, actually in North America at the time. Armed with a broadside of 6-7 68 pounder guns and tougher armour than
Monitor, thus more able to penetrate
Monitor than
Monitor is to penetrate her, it's easy to see who would win that clash.
As for the logistical issue, it's worth studying how the Royal Navy handled logistics in the Crimean War - the main problem there was actually a coal glut - while anyone proposing invading Canada to get rid of a RN base should actually plot out how difficult that would be. Question one: how do you cross the St. Lawrence, the Royal Navy can actually reach it?
(As a side point, the difficulties of the US in sustaining overseas operations are not actually very illuminative - the Royal Navy was
the premier service in being able to supply coal to overseas coaling stations for the entirety of the steam-coal age, while the US was new to the whole thing. I can provide citations if desired.)