The return of 25th December 1814 shows 48,163 regulars, excluding ca. 4,000 select embodied militia and 3,000 Marines. This is the return for America Command, and excludes West Indies Command which has ISTR some 30-40,000.
On the Peninsula (Portugal Command and detachments of Mediterranean Command), 211,000 British rank and file served, exclusive of the Portuguese Army. Wellington's army (including it's detachment at Cadiz) had 65,037 British officers and present under arms in April 1814. Adding the detachments of Mediterranean Command (The Division at Gibraltar and the Corps operating in Eastern Spain), the Lisbon garrison and Marine forces ashore strength is around 90,000. He had some 50,000 Portuguese regulars incorporated into his forces (and paid for and supplied by the British), plus their reserves etc.
Britain sustained a major force (120,000 including mercernaries under British pay and supply) in the Crimean not a decade previously. In 1859 the British are prepared to immediately deploy 6 infantry divisons of 6,000 each.
At home (with outposts in the Med) were available for immediate combat deployment (reinforcing the Division stationed in Canada) 6 cavalry brigades and 6 infantry divisions with their supporting arms. This is short of the target (10 deployable divisions), but made up by the fact that the Militia is still partially embodied, 28 militia infantry regiments are on active service in February 1859.
There is no National Guard until the 20th Century. There is the militia, and it varies from state to state. The loyal and border states had an effective militia strength of 41,190, of whom nearly half (19,000) were from New York. The disloyal states would only add another 10,000 or so.
Men on paper is one thing, the effective strength of neither came up this quickly. For a start, the combined US simply doesn't have that many firearms, and had to buy them from the UK amongst others. The US had roughly 500,000 muskets in varying conditions (60% of them were of War of 1812 vintage and often unusable), virtually all smoothbore and some still flintlock and some 44,000 .54 "Mississippi" rifles. The M1855 Rifle-Musket had only recently gone into production and only a few thousand were kicking around. The US has around 150 field-pieces available for field duty, but they're all pretty old (only 4 working M1857 Napoleons exist for example), the bulk are old M1835 6 pounders and their associated howitzers, even the lighter M1841 6-pounder is fairly rare. They're totally outclassed by the modern British P1853 9-pounder, and even more by the newly adopted P1859 12 pounder breech-loading rifle.
From their standing start of some 50,000 militia the US might produce 100,000 militia in three to six months, which isn't enough even to man their coastal fortifications.
BTW Peak effective strength of both sides was in mid-1863, when the Union had around 350,000 actually in their armies (rather than on paper) and the Confederacy had around 275,000 actually with their armies.