I have close family and friends living in East London, where you have the biggest Indian Muslim community outside Blackburn in Leytonstone, living alongside one of the biggest Pakistani communities in Walthamstow. The marriages between them do happen, but they are very, very small number. Like you said it's mostly Indian girls and Pakistani boys, you get the odd Pakistani girl but it is very rare. Pakistanis would simply be up in arms over an Indian Muslim male asking for their daughter's hand, it won't be entertained. For the most part the Pakistanis in the UK also hail from AJK region and they have very negative view of Indians period.
There are big differeces. The problem is that the Muslims who were close to Pakistanis i.e. the folk of East Punjab left during the partition. You have some outlying communities in the North of India, and of course the Kashmiris. Truth being told they have virtually nothing in common with the Kashmiris, Darda folk, Baloch, Pakhtuns, Punjabis and Sindhis. There is some common ground with those who migrated, for example my ex boss was from India, Hyderabad, and he had very close family in Karachi and had visited Pakistan many times.