In this case there’s no reason not to accept offers at both. That’s necessary if you have a conditional offer in the UK because you won’t have a confirmed place until July or August. It can also be the case that some UK universities won’t decide to make an offer until mid May. Then you’d have to accept your US offer by May 1 otherwise in most cases it will expire. UK universities don’t ask for a deposit, but you will lose your US deposit if you decide against attending.
There’s a separate reason why you might have to place multiple deposits in the US, and that’s when colleges require it in order to register for a room. Sometimes the room deadline is early (in March or April), other times the order of room choice is based on when you paid the deposit. That’s sharp practice by the colleges concerned, but usually they make some or all or the deposit refundable if you withdraw by May 1 (or soon after). Arizona does this for example, and allows you to get the $400 deposit back (though not the $250 housing reservation fee) until May 15.