There are Advance tickets from Grays to York at £29.75 single if you connect onto the stopping service from London to York.
To get these tickets to appear, book on www.eastcoast.co.uk and after entering your journey details, instead of clicking 'Search', click 'Timetables only' and on the next screen enter Grantham as a calling point on the left-hand side. Click 'Update' and then when the page has refreshed click 'Buy a ticket'.
The £29.75 tickets are available leaving Grays at 7:30 (arrive York 11:31) or leaving Grays at 9:29 (arriving York 13:31).
The cheapest fare is likely to be an Advance fare for the journey. For the day in question, there are still some available at £38.15 for the 1127 departure from Grays arriving York at 1450, bookable at www.eastcoast.co.uk. This is a very reasonable price considering how close it is to the date of travel. You must act fast if you want to get that ticket as it is quota-controlled.
We cannot tell you what the cheapest combination of tickets is as it is impossible to work out, however given the price of the above ticket, I would be surprised if you can find anything cheaper.
Indeed the £29.75 tickets (cheapest tier of Advance through fares) are still available for certain departures at anti-social hours.
To give you another option to the slower London-York trains I posted above, search for Grays to York via Garforth. This takes you via Leeds and then on a Northern service to York. £29.75 Advances are available leaving Grays up to 11:27, however the journey is almost an hour longer.