Hi, ex Council Street Naming and Numbering Officer here, there's a lot of misinformation on this thread.
The naming of streets and the numbering of properties on them is solely the responsibility of the local council, in England the relevant acts are:
TheTowns Improvement Clauses Act 1847
The Public Health Acts Ammendment Act 1907
ThePublic Health Act 1925.
Royal Mail allocate the post code only.
Usually property numbers are assigned in consultation with the developer and Royal Mail, but the SNN Officer has the final call. The primary purpose of the number is to ensure that emergency services can easily locate the property.
Neither you or your neighbor can just change your house number, you have to get any change agreed by your local SNN Officer, who would have to issue official notifications of an address change... It can be done, but only in exceptional circumstances.
OP, in your case, I can see no reason for a change to be authorised as it would cause all kinds of problems with Land Registry, utilities mortgage etc for no good reason.
I agree with posters who think your neighbors don't want an A as they think it might sound like a flat... however I've numbered numerous houses with ABC etc, it's increasingly necessary as large old properties are developed into multiple smaller ones.
Your neighbors could add a name to their address, however, if a property has an official number, RM won't record a name on their database, so if they order something online the house name won't show up when the post code is input.
Your neighbors should contact their local delivery office and chat up their postie.
In short, your answer should be "No".
CocoaGin That sounds mad, call (and I mean call) your local SNN Officer, that's the kind of nonsense I'd have had great pleasure in sorting out, RM customer services can be a pain, but their address managers are, without exception, excellent.