I think Britwife is possibly confusing PAYE withholding obligations with tax requirements.
If you are UK resident (which you will probably be) and an employee you will primarily be liable to UK tax.
This is complex, because if you are coming for less than 2 years you can claim deductions in the UK for housing and travel costs plus you may only turn out to be subject to UK tax on income attributable to UK workdays.
Once you qualify, you can still claim the foreign earned income exclusion in the US so you end up with a potential tax windfall if you can keep the UK taxes low.
Please note this comment only discusses your personal tax, not the company's obligation or the application of English employment law to the contract. The employer also needs advice on these issues so will hopefully pay for personal tax advice too.