Yes, in many cases. If the foreign bank is regulated by the FSA then the compensation rules and claims are exactly the same as for UK banks.
Kaupthung Edge is fully regulated by the FSA so is totally covered.
IceSave is slightly different - it opted for a different entry to the FSA (passport exemption). If that goes bust the first �20000 will be compensated by the Icelandic government, with the UK scheme making the difference up to �50000.
Of course, we don't know if the Icelandic economy could afford the compensation, but as it is in agreement with the Scandinavian countries it should be okay and as the UK government agreed to this scheme it is highly likely that should the worst happen and no compensation be forthcoming from Iceland, then the UK scheme would compensate the whole amount.
So, in brief, Kaupthung Edge is 100% safe guaranteed.
IceSave should be.