Wurding, thanks for your reply. I should stress that there is no guarantee that Benjamin Hall the special pleader was either your man or his father. However, it could offer a way forward if you are otherwise stuck.
I believe special pleaders could practise without having been called to the Bar, but he may have been called later. You could begin with the (printed) Law List for 1811 and work forwards annually until you find a Benjamin Hall listed among the barristers. (There may be more than one.) It should give the date he was called to the Bar and, I think, the inn of court. Depending
which inn of court it was, you could then consult the admission register, some of which are easy to access.
In the same 1811 directory (Holden's) is listed Benjamin Hall and Thos. Lodington, attornies, of 1 King's Bench Walk, Inner Temple - perhaps a candidate for being the son.