This happens all the time.
Just go to the local British High Commission, fill out the relevant form, and pay a fee (around £123 when I last checked). They’ll send you a new British accent in the post within a week (assuming, that is, that you are British).
Be prepared, however, that it may not be the same British accent that you had before—they give you whatever happens to be lying around in the Lost Accents Dept., so it might be Geordie, Scouse, or even Glaswegian. It might not even be stubborn…
And if by chance you find your original British accent again, you must hand it in to the nearest British embassy or High Commission, or pay a fine. (A British accent is a highly sought-after commodity in the global criminal underworld, and might fall into the wrong hands.)