They'd like a wall mounted one but one quote says they can't have a
gravity fed HW system wall mounted. Any idea why he'd say that?

With gravity circulation and single pipe central heating, you would be
strongly recommended to upgrade to fully pumped twin pipe system. It will be
difficult to install any new boiler into your house whilst not breaking
building regulations, let alone a modern type. Soon it will be absolutely
impossible, as only modern condensing boilers will be allowed. These will
not work with gravity flow.

Your fears of combi boilers are unfounded. The main problem with them is
relatively low flow rates. This won't matter if you only have baths
infrequently. As your storage system is seriously non-compliant anyway, it
may be the cheapest way of getting up and running again.

Whilst I can't see that single pipe heating circuits are specifically banned
at all, you are required to have separate heating controls, such as TRVs in
each room. I don't know if you can get TRVs for this type of system, which
have not been installed in the UK for many years (decades).

Christian.