It's do-able, or at least it was in 1998. I worked the first 6 months of my time in the states as a UK employee (L1 visa), then transferred over to the US payroll. I think it's covered by a tax treaty between the US and UK, but there are limitations, I don't think you can do it indefinitely.
So it's complex (or at least it seemed that way to me) – My company paid accountants to handle my UK/US tax returns for that first year. So I never really found out that much about it. A couple of things to think about though… You might want to keep paying NI here so you can qualify for a UK state pension – even if you aren't planning on coming back, it's something that I wish I'd done (ended up coming back to the UK after 6 years). Also don't forget about State income tax, I don't think that's covered by the tax treaty.
Bottom line, if your employer wants to keep you on as a UK employee, have them stump up for an accountant to sort this out for you.