I've read more than once that the smallest cathedral in the United Kingdom is in Carlisle, Cumbria.
I've also read though that the smallest is actually in Oxford. Can anyone solve my dilemma? Please? Which is it?

No idea! What I found, after a quick 10 minutes searching, are the following claims...

Carlisle Cathedral, built in 1122, is the second smallest cathedral in europe. Also described as one of England's smallest.

Eglwys Gadeiriol Llanelwy ,Saint Asaph Cathedral Church is the smallest cathedral church in Britain.

The Cathedral of The Isles, Britain's smallest cathedral, is on the Island of Cumbrae.

Christ Church Cathedral, Oxford is the smallest Cathedral in Britain.

Sadly, none of the websites provide any evidence at all as to why they claim to be the smallest.

I can't answer your question for sure, but the cathedral in Oxford that claims the title is Christ's Church or Oxford Cathedral.
This page estimates it's present size at 16,413 square feet, and puts at least 4 cathedrals smaller than it, Carlisle not among them.
This page gives a floor plan for the Oxford Cathedral, with scale, and refers to it as the smallest Cathedral in England.


This page gives the dimensions of the Carlisle Cathedral. I'll leave the calculations to you.

It seems like you are running into the same problems I run into when trying to check some Trivia. Frustrating, isn't it?