Historically you will find loads of players that would have improved England.
I'm not so sure all in all the difference is sufficiently relevant to introduce division and/or the dilution of commitment to the cause. Take peak Scotland, move the likes of Hansen, Souness, Strachan, Dalglish to Team GB alongside Butcher, Robbo, Hoddle, Lineker... would it work?
Spain always struggled with this.
A GB team would have won a shitload not because of the extra players (although that would have been nice), but because we could have had a Scottish manager.