I don't specifically know about the BA 319 CE but, in most planes I have been in, the bulkhead and exit row seats have non-movable armrests, the other seats have movable armrests.

It seems to me that since BA CE seats are the same as BA ET seats with just the midddle seats blocked for the changeable area assigned to CE, the armrests should be movable in most of the seats.

If nobody has a better answer after some reasonable time maybe this question should go to the BA forum where more BA flyers will see it.

I hope they remove your cast pretty soon.