Dear OP,
There’s an enormous amount to unpack here, beyond me. You say that your cousin and potential husband is “decent” but only that he’s “from what [you] understand, open minded”.
That doesn’t suggest to me that you played together as children on holidays, or really know him all that well. Surely you would know very well where he stood?
If he were all of these things (decent, a scholar, a rich man, of tolerant and modern views) AND you had known him since childhood or for many years, perhaps you could do worse, but it’s incredibly unwise to marry someone you have perhaps only met a few times.
An open-minded man in a deeply traditional society might still strike you as more conservative than you would care to marry.
I am neither a Pakistani nor a Muslim but I should like to point out that you cannot, in this country, be compelled to wed, nor can you be removed from the country to do so.
Any religious contract, bride-price payment, or so on is almost certainly flatly invalid in British law and binds you not a jot (although I imagine any solicitor would gladly reassure you in a more learned way than I).
It’s a horrible thing to have to say but perhaps necessary, if not for you as a graduate but for a young lady who might read this in a more precarious position.
Αs long as you are at present quite safe, I think this goes well beyond what we can advise. At the very, very least you need to see more of this man in a British context, and not making the best impression he can, but as he really is.
I understand that there are religious restrictions in strict Islam on the sexes meeting unaccompanied, but could you perhaps find a sympathetic companion to meet this man on neutral ground, as it were, for some good period of time before making a decision? If he is a rich man, he has little excuse not to fly over.
My only advice as a stranger is to do nothing rash, and nothing for the sake of duty that goes against your heart.
If there is even a trace of coercion, get out.