If you become a resident in the UK, you will need to pay UK capital gain tax on the sale of this house as this is going to be considered an investment property for you and not your principal residence. As this gain needs to be reported on your US return also, you can claim a credit for the UK taxes that you will pay in this case on your US return thereby avoiding double tax.
If you remain non-resident of the UK, there is no UK tax liability. However, you will pay US capital gain tax on the sale. No foreign tax credit available in this case, as no UK taxes have been paid.
So really, depending on your overall effective tax rate, you will be paying tax at the higher of US or UK capital gain tax rates whether you become a resident or not.
Please feel free to call me to discuss this further of you like more elaboration on this issue.
Helen