It most certainly is not a DIY job. Tell you what, call them again and tell them you've bought a box and are about to change it and you just want to check which electric cable goes into which hole in your meter and ask them where the big black thing with the 100A/80A fuse in it goes after you've taken it off the wall.
Better yet, tell them you've done it but had a few bits left over and ask them if they want their meter back as you didn't think it was that important.
Have an inflated paper bag at the ready and pop it whilst giving a running commentary of your DIY'ing.
I've never heard anything so ridiculous and down-right dangerous!
What condition is the board the metering and supply equipment is attached to in? If they're bad it can constitute a dangerous installation and require attendance by the DNO (electricity network provider) for your area to rectify.
You may find yourself in the position of having to liaise with and co-ordinate the attendance of the DNO to safely disconnect/move/re-install the cutout (main fuse), a builder to install a new box and the energy supplier to re-connect the meter.
If the gas is in a plastic, outside box then just fitting a new door is usually a simple task and DIY'able. But they come in different sizes and different hinge configurations (sometimes an actual hinge, sometimes pins) - so measure it. Check the box too - if it's damaged where the door attaches/locks, you may not be able to fit a new one and a new box will be required.
https://www.meterboxesdirect.co.uk/gas-meter-box/gas-meter-box-door.html
It can be a grey area and energy suppliers can be helpful or not, as you've discovered. When I worked for BG I frequently had to abort meter exchanges due to insecure, sometimes downright dangerous, installations or simply because there was no door on the meter box. Technically, it's down to the person responsible for the property, whether that be the home-owner, or landlord, but we could (but didn't always) order new doors and go back another day, fit the new door, and perform the exchange. I think it was usually done when our completion rates had been low and it was otherwise a quick and easy job.
If the meter board was falling apart and there was nowhere to safely fit the metering equipment, or safely pull the main fuse (they can be stiff and there's a risk of the whole cutout coming off in your hands if the back-board is rotten - and that's not fun!), then the matter was passed to the DNO to replace the board. However, they frequently tried to wriggle out of it, or did the very bare minimum to make it safe.