Unfortunately, you cannot fit a timer or room stat without removing the case, which you should not do. The instructions state that you cannot interrupt the mains supply with timer/room stat - there will be a pump over run which requires a permanent live.
I understand that arguing with a LL is a pain, and I know some will worry about losing their home.
You could complain to the local council, there will be a department responsible for ensuring houses are to a certain standard although I don't know how they would react.
Is the agent a member of the trade body? It could be worth looking at that.
This is the install instruction book, and should be left with the boiler. Do you have a copy? it will state somewhere in there about controls , and there is a benchmark certificate at the end - the installer should have completed it.
https://www.glow-worm.co.uk/glow-wo...tion-and-maintenance-instructions-1948957.pdf
I will try to find the documents that you need to argue the case. LL's like yours make my blood boil, tbh