The UK is prohibited, under EU privacy laws, from making UK criminal records freely available to overseas agencies. So (at least theoretically) the US immigration service can't directly access UK criminal records.
However a great deal of information is undoubtedly passed on in the guise of 'anti-terrorism'. The UK is permitted to pass on information in response to a specific request from the US authorities (rather than on a 'carte blanche' basis). With the introduction of the ESTA system, for travellers who've not obtained a visa, the US authorities might be making such a request in respect of every traveller, thereby bypassing the normal rules.
Here's an analogy:
Our police aren't normally allowed to stop and search people at random. (They have to suspect a crime in order to do so). The only exception is in an area covered by a temporary order (which can't last longer than a fortnight) issued under anti-terrorism legislation. So, last year, the Metropolitan Police repeatedly applied for the renewal of such orders throughout the entire year, covering nearly the whole of London, and randomly(?) searched 130,000 people. I'd be very surprised if a single one of those searches had anything whatsoever to do with terrorism. It's just a way for out police to bypass our normal civil liberties. So, if our own police can use 'anti-terror' rules to get round UK laws, it's certainly possible that the US authorities might be applying similar methods to bypass EU laws (which, after all, they'd rather not recognise anyway).
Chris