To "go to Finsbury Park" means to go all the way on a first date. It is implied that kissing, cuddling, conversation, dinner, touching, oral sex, spanking, reading and skinny-dipping are all skipped in favour of full-blown, uninhibited sex.
"How was your date last night?"
"Astonishing. I thought I might be allowed to cop a feel, but we went all the way to Finsbury Park!"