On all Cross Country and LNER services there is now a weekday (Monday to Friday) First Class upgrade available. Buy on the train from the guard if there is space available. On LNER that is almost never a problem. On Cross Country that is more of an issue.
On LNER it is a flat rate of £39 between Doncaster (and all stations south thereof to or from Kings Cross). To all other stations (so York Edinburgh or even Inverness) it is £49.
On Cross Country it varies by distance, but for instance from Bristol to York (a common journey on here, originating on GWR at Bath) it is £35.