UK isnt fully part of EU exactly, a more apt analogy would be say France and Bulgaria. And yes they would need to conform to both EU and Bulgarian law, but that is the case for any federation. Pakistan similarly has provincial laws and federal laws.
a minivan company can be owned by a Punjabi, but when he drives his vans in NWFP he needs to turn off the music.
It is much more then just turning off music , or taking a chaddar in NWFP. It's about paying them handsome royalties for Sui Gas, using Makran Port, Minning for Coal or using their Highways to connect to Central Asia/Iran.