Hi Neil and Kay,
There have been similar threads if you search. Try "Tracfone" and you'll probably get the threads.
Tracfone and AT& T do pay as you go systems. The phones can be bought from Walmarts , mall outlets and AT & T shops or over the internet (which ususally requires an address in the US where the phone can be delivered.
We have had an AT &T "Go" phone for the past couple of years. You buy the phone in a pack with the sim etc for about $90 and then top up with service charge - $19.99 / $29.99 etc which gives you so many minutes (Similar with Tracfone)
Main difference with UK mobiles is the US system minutes run out after around 30 days and the sim cards after 45 days unless you have a direct debit to keep the service running - or pay for a yearly subscription.
With our Go phone , we take the phone to an AT &T shop on arrival and they give us a new sim card free and we just buy top up minutes. Downside of this is a different cellphone no. each time , but we don't mind that.
If you have a triband UK mobile you can use that in US but calls are routed via UK from US providers which is expensive. (I've even swapped the AT &T sim into my UK quad band phone and it works OK for calls but you don't get all of the GPS services)
Have a look at the Tracfone website , but be aware that the "special offers " are reconditioned phones and again you will need an US address.
Regards