You can ride on the towpath to Thatcham easily, after which the Sustrans route diverts onto minor roads for a bit, then back onto the towpath to the centre, but i bet you could steadily ride the towpath/footpath section in between with no problem.
Done it both in summer and winter; it’s better when dry as there are some unpaved sections across fields, which when dry have little ‘singletrack’ trails across them- ideal for child cyclists! There are a few gates which take some maneuvering with a trailer/tagalong, if you’re towing kids. There’s a carpark at Theale lock to start from.
Stop at Aldermaston Wharf cafe for coffee and cake on the way. (take cash) Job’s a good ‘un.
You’ve given me an idea to do with the kids at the weekend now!