I had a bullpup a few years ago, it was custom built, based on a BSA action.
I found it was good for hunting because it could easily be rested on my knee, handy when there is long grass etc. Sadly I don't think you are allowed to rest your rifle on your knee in HFT, so that would be no benefit.
Standing shots were ok, I can't remember being any more accurate with the pup than I am with a well balanced rifle (i.e I am equally rubbish with both).
Where the pup did not work for me and one of the main reasons I got rid of it is the action is too short to hold on an HFT peg to get it stable. With a "traditional" rifle the action and stock is longer, allowing you to support it far forward of the trigger area, giving you a very stable platform. The pup was waving around all over the place because you are pretty much holding the stock against the peg near the trigger.
So for wondering around on a permission and taking (non-legal UKAHFT) kneeling shots, shooting from a vehicle or a hide, it was great, for HFT no good for me.