British Lancers existed, just not during the Napoleonic Wars; mostly before and after.
http://en.wikipedia.org/wiki/17th_Lancers
Some regiments were made Lancers in 1816, a year after the Napoleonic Wars ended for good. The 17th were in India at the time, so they didn't even realise they'd become lancers until they returned to the UK
Wikipedia is actually pretty legit now. Also I was referencing British Gendarmerie like the RCMP.
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I don't think the Mounties saw much action in the Napoleonic Wars. Not being formed would definitely contribute to that.
The actual Yeomanry in Britain wasn't deployed either, if you look up the Peterloo Massacre you'll see a good reason why.