You definitely can file as married filing separately and not include her income (if any in the UK) on your return. You will need to show here name on box 3 of 1040, and write NRA (or non-resident alient) after her name. Also you must not claim her as a dependant. You will not need to apply for an ITIN.
You probably already know that if it makes an impact to your bottom line tax (ie provide you with a lower tax), you have the option of making a claim to treat her as a US citizen for US tax purposes and therefore be able to file jointly and benefit from joint tax rates, higher standard deductions, etc....