N1
I don`t think that "pure" Swiss pilots are flying for Speedbird yet.
If you got Airbus 320 experience and a JAR ATPL you might have a chance to enter as direct entry First Officer. BA wants you to transfer your JAR ATPL from the FOCA to the British CAA before you apply!
Furthermore, and I dont want to be offensive, make sure you have an excellent command of English. The standard Swiss/ Swissair English is not sufficient, write the CPE (Cambridge Certificate of Proficiency in English) and adopt something like and an "English" accent.
If you are an Airbus pilot you might initially have a chance with Virgin, especially when you are typed on A340, or My Travel, Monarch, easyJet etc. After having established yourself in the U.K. a transfer (i.e. to BA) becomes much easier.....