OK. I measured out the distance and went out to find some options at the shops. I came back with a long cable and a connector to allow me to have RJ12 on one end and RJ45 on the other. As I was mucking trying to sort out the tidiest route to run the cable I tried one of the other sockets in the house, which also worked.
Then it dawned on me that the socket I had just tried was an RJ12 not the RJ45. I could run the big long cable without connectors (less signal loss) and put the routers exactly where I had planned in the first place.
Bonus was that the cable would run around the rooms in such a way that I wouldn’t be crossing (and likely tripping or pulling them out) the cables very often.
And all was good…..