Mogweed brought next idea :
I've been told to stay away from the cheaper ones but that's about all I
know, so can someone recommend a good, reasonably priced, cordless doorbell?

Friedland. They come in various working distance ranges, the further -
the more expensive. Range is open space range and will reduce
drastically with walls in the way. The two (or more) parts have to be
matched with a switch entered code, to avoid next doors push sounding
your chime, though later ones do the matching automatically. Top of the
range is about £35. The chimes can be mains powered with an adaptor.

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Regards,
Harry (M1BYT) (L)
http://www.ukradioamateur.co.uk