I'm with O2 and they have a deal whereby you can use your mobile phone in the USA, same as you would at home, for 4.99 per day. I'm sure other companies offer something similar.
So for a week, it'd cost you 35 quid and you'd not have any of the hassle of switching SIM cards and numbers.
And if you use WhatsApp for calls, you've got no cost anyway, as long as you've got access to WiFi.