No. British war planning against the US was about protecting Canada from American encroachment. This is true both in the antebellum era after the Fennian raids and during the civil war. Indeed, Britain repeatedly resolves border disputes with the US in a peaceful manner, negotiating treaties to restrict naval forces in the great lakes in 1819, peacefully resolving the Arostook war in northern Maine, negotiating the BC/Washington Territory border in the 1840's and negotiating a resolution to the San Juan border dispute after the pig war in the 1830's1850's.

Moreover, Britian had no intention of 'reclaiming' America -during- the war if 1812 - British Military operations were aimed not at invading and occupying the entirety of American territory, but forcing America to sue for peace on favorable terms (and taking pressure off of Canada). Even though Britain in 1814 was burning the White House and invading through Lake Champlain, British diplomats were even then negotiating for peace in Ghent. The most British negotiators ever demanded was an American Indian buffer state in the modern day upper Midwest. There was never a serious intention to 'reclaim' anything, only to contain American expansion after the US had invaded Canada. Again.

Now there were a variety of crises between Britain an the US, but there was never a serious threat that Britain would 'Reclaim' their former territory in North America.

EDIT: Please see Irishfafnir's comments below for a correction regarding the territories that Britain demanded during negotiations at various points - territory on the American/Canadian frontier.

Sources:

Howe, What Hath God Wrought

Wood, Empire of Liberty

Snow, When Britain Burned the White House (bit of a popular history, good overview of the Chesapeake campaign of 1814 from a British perspective).