Your calculations seem to be right. I got the same answer
Freely place the first british team: propbability 1 free spaces 3x2+1
British teams together: probability 1/7 free spaces 3x2
Freely place Spanish team: probability 1 free spaces 2x2+1
Second Spanish team not with the first one: probability 4/5 free spaces 1x2+1+1
Third Spanish team with neither one of the Spanish: probability 2/4=1/2

So a total of 1x1/7x1x4/5x1/2=4/70=2/35 which indeed is approximately 5,7%

I just saw it now since I was in school before. Well done!