I remember when we joined the EU that suddenly bands like Gong (who were formed in France) were suddenly regularly touring this country, which was a good thing, as Daevid Allen had been refused re-entry to the UK after Soft Machine toured in Europe.
I think the usual way things were done before then, aside from the visa palaver, was that the respective national musicians' unions would make sure there was tit for tat regarding the number of musicians allowed in and out. The same for US musicians (so I would guess most UK bands would head to the US for the better swapsies) which is how some blues artists like Big Bill Broonzy ended up coming over to the UK alone, as they could then come into the UK as an entertainer rather than a musician.