Or you could look at Lumo.
No point to that, as Lumo do not call at York.
This is at the limit of 12 weeks advance booking. The delay in opening bookings is that the line is CLOSED between Peterborough and London Kings Cross- https://www.nationalrail.co.uk/engineering-works/kgx-pbo-20250517/
All trains will terminate at Peterborough with bus replacements to Bedford for East Midlands Railway (EMR) or Thameslink trains to London St Pancras. For an all rail route- Change at Doncaster for Northern trains to Sheffield for EMR to St Pancras. Or there are a few York to Sheffield direct trains Northern trains or an hourly Cross Country train to Sheffield for EMR south, at least on the Saturday.
The northern trains won't open up until 8 weeks before travel.
Or York to Manchester on TransPennine for Avanti to London Euston- but TPE also have amended service (still running, but on a diverted route).
EDIT- East Midlands Trains Advance Tickets for that weekend are open now from Sheffield. as are Cross Country York to Sheffield.
Book those as separate tickets (not a through ticket) and you can do the journey for under £50 (some trains as low as £35) before railcard discounts.