You CAN fly any G-reg but are limited to day VFR within the UK ( the UK being the only country in Europe to recognise the FAA ticket w/o any further paperwork).
No doubt 2 Donkeys will be along shortly to remind you that there is no "Day" restriction. It's simply restricted to VFR.
There is also no "within the UK" restriction. The CAA validates automatically (without paperwork) an FAA licence for flights in a G registered aircraft worldwide, not just the UK.
Also the UK is not the only country that recognises the FAA licence without any further paperwork. The Irish Aviation Authority also recognised the FAA licence without any paperwork, but in this case, there is a Day restriction, and there is a "Republic of Ireland only" geographic restriction.
dp