Try Servisair or Aviance at BHX... they'll be recruiting pax services staff shortly for the summer season (probably)... if you get in, they'll give you most likely a part time position, if you're lucky, full time for the summer season, don't be under any illusions about the pay - it aint great, but everyone has to start somewhere!
If you're any good and they have the vacancy, there's a possibility they'll keep you on after the summer (March-October)... once you're there you'll have a better idea of what you want, but as far as Dispatch is concerned - see the post above this one! The tour operators do have staff at many airports, however, they don't have many - maybe one carrier'll have 3 or 4 only as the handling agent takes care of the rest....
Best of luck!!
JFF