berryplucker is correct, no double taxation if you are non-resident. To quote the IRS “If you remain resident in the UK for UK tax purposes, normally you will be taxable on your income arising in the UK and overseas.†If you become non-resident, you will normally only be taxable on your income arising in the UK.
So it really depends on your residency status. As long as you inform your Tax Office and ask for a form P85 and leaflet IR138 telling them you are leaving and you are taking a full-time job abroad you can be a non-resident. Basically you need to be out of the country more than 182 days in the year to qualify as non-resident and therefore not liable to UK tax.
Check out
http://www.inlandrevenue.gov.uk/nonresidents/ for lots more info
You are still liable to tax on income arising in the UK however, such as rental income from your flat if you choose to rent it out rather than sell. In practice you can claim enough expenses against the rental income (up keep, trips back to check the flat etc) that you would not pay tax but you must make a declaration.