I dont think there is limit, you can transfer through banks or exchange companies like Dollar East etc. exchange companies charge bit less compared to banks. and also are quicker.
normally from UK to pak this much amount cost is £30 pounds or so through banking channels and money is there in 5-7 working days
I usually use UBL clickremit site to send personal fund to Pakistan. My limit was USD7000 per transaction. After patriotic act, it was reduced to USD 2500. Though I never reached my limit.