That's a lot of travelling for a short stay! The cheapest advance tickets at £77.40, with plenty of services to chose from.
For £69.80 you could get an off-peak day return to Newark stations (£26.80) and an off-peak day Newark stations to London Zones 1-6 Travelcard (£43). Your York > London trains must stop at Newark and there are some off-peak restrictions. The East Coast journey planner can confirm which trains it is valid on, and it seems to fit your journey. You should be OK using it on the 12:00 from York (arrive Kingswood @ 16:02) and on the 17:57 from Kingswood (change for the 19:33 from Kings Cross, and again at Doncaster for the 21:39, arriving 22:01).