I plan to travel with my family from London to Glasgow and back during the summer. I will be travelling by train or other public transport. I would like to make a few overnight stops on route. Perhaps cutting the journey into 3 parts. Can anyone suggest a good itinerary of places to visit on the route north and south again. The places must be accessible by public transport without too much detour from the main route.
I've not stopped much on the west, although can recommend Cumbria - or anywhere in the Lake District really. So Carlisle - very nice town. Part of the start of Hadrian's Wall, which is pretty great to see and walk a segment of.
Up the East Coast is another option - you could stop in York, and Edinburgh, before crossing over to Glasgow. Edinburgh speaks for itself - spectacular castle, amazing old town, so much history.
York was a Roman town and the York minster is very special. The city itself is very compact and still has some of the city walls, as well as many old - OLD parts worth seeing.
Aside from Hadrian's wall, all of the above can be accessed on the train line and with minimal walking. For Hadrian's wall you may need a car, we had cars - but there might be public transport or a tour.
Apart from other suggested places, consider stopping in either Cambridge or Oxford - these are really nice, historic towns. It is certainly easy to get there from London, you would have to check the onward transport to your next destination. Probably it will be not that hard to get to Birmingham from Oxford.
Some people recommended Liverpool, but I haven't been personally.
Further on north there is the Lake District, which is very nice if you are into hiking. Visiting it in one day without a car might be rather tricky though.