Impressed? These were soldiers of the various german states who remained as such (of course German recruitment methods varied from good pay to outright impressment and most shades in between) and came under British command as bodies of troops of foreign armies in British Pay. It is not as if the British army wandered around Germany impressing passing peasants by force.
Poor choice of words. The correct term would be "Hired". The German states, including Hanover, routinely impressed criminals, the homeless, foreign travellers, anyone they could without harming the economy into their regiments.
Hesse in particular was notorious for this (hence the "Hessians" of the American revolution).
They german states then "Hired" or "Leased" or "Loaned" these Regiments to the highest bidder during European wars. This was an age old custom and a great source of capital to impoverished tiny German princes. The soldiers themselves weren't mercenaries as they never sold their own services.
Hanover "Loaned" soldiers to Britain on a regular basis, often forming a substancial portion of the British forces. They were able to recruit/draft/impress cheap soldiers on short notice without the burdens of British political opposition.
In 1776, a great reinforcement of 25,000 soldiers hit America. 3/5's were German. None were from Hanover but Hanover's men were utilized in European British areas (Channel Islands, Minorca, Gibraltar, Ireland) and freed up soldiers.
Without the Germans as a whole and Hanover in particular, Britain's effectiveness in wars from 1700 to 1815 would be nearly negligable.