The estimated time of processingly a new passport holder's application in the UK is six weeks. It took me less than three, and that was with the interview-arranger's warning that I would have to wait an extra week for my interview if I went with the central London interview office instead of one of the county ones. (Interviews are now - as of a couple of years ago - required of first-time passport holders in the UK.) My new passport came by special delivery this morning.
Now going to visit Wales really would be entirely for the fun of it, and not in the least an act of symbolic rebellion against travel limitations.