Hi Mutley
If I understand your question correctly you have a slot around the inside of the opening in the door where the timber was removed. If this is the case it would be safer to remove the doors and use a router on the outside or inside to change the slot into a rebate so you can fit a piece of glass of a size just a little bit smaller than the bottom of the slot ( now a rebate ) This would give good contact and support for the glass all the way around ( 10 mm if I understand you description correcly,
Then you can put putty/ silicon all the way around and put in a beading to hold the glass in place
If all this makes sense then you would need a piece of glass 1100 +10 + 10 minus 2mm to allow for inaccuracies in the frame and 240 +10+10 minus 2mm wide
It is important to check the diagonal measurements as well as the door may not be square and the glass will not fit!
What sort of glass are you going to use? The last time I replaced external glass in a door the replacement had to be laminated.
Hope this helps
Cheers