Well, I showed the RBQ-style question in the previous post to a colleague who pointed out, in a reasonably gentle manner, the ways in which it didn't quite make the grade. Luckily, another was nearer the standard set by that BBC Radio 4 programme so I shall reproduce it below. It's probably fair to say you will need to be of a certain age, and to be familiar with 60s British pop entertainers, to have a fair chance of solving this, but when you have solved part then the rest ought to fall into place fairly easily.
And my colleague suggested that the real test of a Round Britain Quiz question is that the answer, when revealed, ought to make you exclaim in delight: "Oh, of course!" I hope the following offers you that possibility.
If you can name Joe Brown's would-be christener and a rank and enseamed hat model then locate precisely the attractive Pirandellian health worker hymned by Macca why might it be a circular journey?