Since I started this thread, I should add some comments on our experience with Roam Simple.
In my view, price (SIM and the refurbished phone) was reasonable, phone and SIM were delivered very promptly.
We didn't do a whole lot of calling while we were in the UK. Our bill for calls and texts came to about $12.50, less than the cost of a round of "sticky toffee pudding" desert for the three of us.
It was very handy to know the phone number ahead of time -- we were able to email it to relatives who were then able to get in touch with us (free incoming calls) immediately upon our arrival.
In some of the more remote parts of the Highlands of Scotland, signal quality wasn't as good as we get at home, but that was due to being remote. In the cities, the T-Mobile network they use was just fine.
We now have a phone which we can get SIMs for, for future trips. We took digital pictures of a few of the text messages we got, since we won't be able to access them here.