Thank you for your reply and input, Bob. My employer is a bit of a gem and has been happy to discuss all possibilities. I don't think this particular solution is viable because we don't have very much outside space and our neighbours are less than accommodating. It was after a fairly exhaustive discussion exploring all the options that I came to a conclusion that a new bike was actually the most sensible option. I have teenagers at home all enthusiastically claiming dibs on mum's old bike, so it won't go unloved.
Your answer did get me thinking though. I work in Southport which has a secure cycle shelter, which is just round the corner (well a cut through Marks & Spencer!). I don't know whether anyone on here has experience of it. I went to look at it today, unfortunately too late for there to be any staff to talk to. It does look really secure and is entirely under cover. I think it is free to use, you pay a deposit for a key and then lock your bike to the racks inside. I'll go again on Thursday and chat to the staff to ask if there is any possibility of charging the bike in the shelter, probably not but worth an ask.
If not, I will be looking for quite a different replacement bike. Would still like it to be a bit lighter but the main feature would have to be easy to remove battery so I could take it to the office for charging. My preference then would be for something that looked gorgeous and ladylike.