Dowehave,
3K GBP in the US would be scraping in, it's realistically a little more when you add in living costs , accom, and travel espenses. That said however you can do it in one sharp shock and get it over with.
The downside here is obviously the weather, and you may find that as you get nearer your flight tests that time indeed becomes money here in the UK. 4K sounds about right if you are flying 152's or pa-28's.
Oh and pay as you go!!! never pay up front.
cheers
fw