Of course I’m not 100% sure but I think Toshiba doesn’t have old international warranty anymore so I think US warranty will not cover you in UK but for this you must ask Toshiba US.
What you can also do is to ask this on US forum, just to be sure about that -
http://forums.toshiba.com/t5/Laptops/ct-p/c_laptops/tshb
If you will get more info please let us know.