York train station

There are no luggage lockers anywhere on the British rail network, a souvenir of the Northern Ireland Troubles.

I do not know of a left luggage facility at York.

Be sure that your train ticket allows a stop.

Here is a company near the York Minster that will store your bag.

https://www.yorbag.co.uk/

I am sure there are other commercial entities that will provide this service.

we were there in June and leaving the train station there was a sign on the sidewalk advertising left luggage. It is this company, just a 2 minute walk from the station: http://www.leftluggageyork.co.uk/