Should I keep my savings in my US or UK account?

My boyfriend and I have begun saving up for our unmarried partner visa. Since he's getting a PhD grant and is not allowed to work until he finishes, we're aiming for 4000 GBP between us when we apply as proof of our ability to suport ourselves.

I'm wondering if I should keep the money in my US account where it is currently, or if I should start moving it incrementally over to my UK account to lock in the relatively favorable exchange rate. Would it make a difference? I know wiring money overseas costs money, but it would also be easier to access it once I'm in the UK. Or maybe half in one and half in the other. Hm. I don't know. Anyone have any experience or thoughts on this sort of thing?

Thanks!

Woah, I just looked at the exchange rate and it's down to 1.39 GBP to 1 USD?! Holy cow. Maybe I should keep my money in my US account after all...

You have it just a bit backwards.  According to XE.com the exchange is 1 GBP = 1.39526 USD.  I would say in either case it would depend on the interest rate you are able to get.

i'm not sure...   

i will be converting USD to GBP in March-April for need not trying to time the fx...
1.40 rate would be good... hoping for 1.25 or less!!  .... but will settle for below 1.50

You have it just a bit backwards.  According to XE.com the exchange is 1 GBP = 1.39526 USD.  I would say in either case it would depend on the interest rate you are able to get.

Ah, yes, that's what I get for trying to post late at night when I should be asleep!