Have her neighbours got one - could the sound be travelling through the wall/pipes? That doesn't explain the speech - but there's sometimes a sort of whirring noise between the cuckoo notes
Has she ever lived in a house where there is one? It might be a waking dream - just on the verge of sleep?

I would suspect the former - that maybe her neighbor bought one and put it right against the wall, so she ends up hearing it as well.

The houses are free-standing. Also she only hears it the one in time in every 24 hours.

Whoa, that IS weird. (Potentially kinda cool, too)

She knows her neighbours and I assume she's asked them. Besides, she lives in a free-standing bungalow.

Yes, she has had a cuckoo clock in the past.

Then the waking dream/memory seems a likely suspect. I once got out of bed to go to switch off the cuckoo - then remembered I'd not owned one for several years - and it seems possible that she's misinterpreting the sound between the notes, although her memory recorded it correctly

Can it be heard during the day?

No, only at night- and only once in the night.

After reading all the replies I am now officially weirded out.

Answerphone with a peculiar ringtone?

Which always goes off at the same time? I suppose it could be a neighbour's alarm clock.

A radio alarm clock, set to Radio 4, which is immediately hit to snooze.

While I think it's much more likely that the neighbour has a cuckoo clock, my first thought was that maybe there's a metal piece of the boiler that is picking up a radio signal. I've read about people picking up the radio with metal tooth fillings and stuff.

No, I've just checked: the neighbour doesn't have a cuckoo clock.

Nah. It's a ghost. A ghost with a cuckoo clock. Living in the wall. Well, NOT living...whatever it is that we do when we become specters.

I'd get a tape recorder and try to record it.

Wouldn't it be cool if you opened up the wall and found some really really ancient cuckoo clock--and a big bag of gold coins?

Might as well dream big. :D

This is the best suggestion so far.

Next time I visit I'll take a pick-axe and get those gold coins out. :)

Sounds like it's time for a sleepover.

This is a good idea!!!