There are two issues.
1. Relative to the cost, the AHQ doesn't consider dedicated LIFT/FCU platforms a priority. Some months ago Alan Warnes said the PAF will use FT-7Ps in that role, he was even unsure about the JF-17B (taking on FCU)! Still, the Hawk, M-346, etc are pretty expensive, e.g. 18-24 such planes could run $700 m to $1 bn (albeit with support for 10 or so years).
2. Britain, which - like the US - has been a mixed-bag in terms of being a defence supplier to Pakistan.
The Lynx helicopter saga of the late 1990s was not taken lightly by the armed forces as a whole (esp. the Navy).
Efforts have been underway as of late to normalize defence ties, e.g. Kelvin Hughes radars for the PN's submarines, refurbishing Sea Kings, having Cavalier Group work with Jankel to design the Hamza-series, etc. Even Leonardo's Vixen AESA radar offer for the Block-III required some measure of regulatory approval from the UK (as Selex ES is based in the UK).