Is it just the taxation issue they are concerned about? I'm sure it's possible to work for a company in one country whilst living in another as I've heard of it many times before, but there is such a thing as double-taxation where, as Taffy says, you can be stung for tax in the country you reside in plus the country you have just left. With the UK I believe there's a form you can fill in which lets the tax people know your situation so they shouldn't be looking for any tax from you. It's a way of applying for exemption from paying tax in that country.
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Mother Bear 
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