Not actually heard of any big cat keepers in the UK personally. All I know is that they are DWA listed and will need public liability insurance. I'm pretty sure they only give out licences to zoological institutions though to be honest. It will also depend on whether your local council will allow you to keep one in your area- for some reason it's not a nationalized system and because of the flaws in it, it is basically up to your council whether they will grant you permission. You are probably best off contacting a zoological institution. Can't think of any that have cougars over here though...
Why not ask your aunt and uncle about aquireing a cougar?
First read I was thinking the same thing, just go down to your local cougar hang out, one is bound to make you her pray!