I own my flat in a managed block, and have done for 28 years. Last months I had an inspection of my front door, and the management company sent a letter asking me to make some alterations. Apparently I need new hinges, a device to ensure the door closes itself and the gap needs to be smaller.

What in your opinion would be a reasonable timeframe to make these improvements? They're insisting on three months which I'm questioning. I understand the law changed in 2021 which means they've waited five years before carrying out the inspection.

I believe a door self-closing device to be essential, depending on the door location, and that this part of the "improvements" should be done urgently.  For the hinges, it depends on their condition, if they fail to suport the weight of the door then they should be replaced as a matter of urgency.  

You may find this and interesting read   https://peteapps.substack.com/p/the-door-to-flat-136 

Regarding the gap, it depends how much too large it is, and does it affect the effectiveness of the smoke seals?