What I found about this car is that it has been realized by Laurie Halliwell and Norman Routledge from Leeds, in 1948 or maybe using a '48 TA14 Sports base.
It took one hour and half of googling every option containing the only things I had...Alvis ta14.
Yes, you'd think these things would pop straight up when you enter the name, but they don't always..
Well, you've got the right car, so that answers two of the four questions posed - what it is and what the base is.
But, although Halliwell and Routledge started the project to build this TA14 Special (in the 1960s actually, not in 1948, which was the year of the car they used as the base) they only actually tinkered with the engine but didn't build this body, which was added by a later owner after they had sold it unfinished!
Still some work to do therefore to find out who built the body and when..
I'll lock it for you since you've got so far.