Trip away with 3 kids

[Exactfare]

Is there a reasonably cheap way to do a trip to London or Edinburgh (open to other suggestions ) with 2 adults and 3 kids? Kids are 9-5yrs

We normally go away in our caravan but it's for a big birthday in October

It's the accommodation that's a bugger with 3

It depends on what you want to see and do?
Have you considered York or Liverpool?
Liverpool has plenty to see and do on a city break plenty of free stuff too, it also has several beaches one we often go to for a walk in the winter then the cafe for hot drinks after. Plenty of great value hotels as long as there are no football matches or concerts that weekend. But you can be out of the city in 20 mins opening up more cheap accommodation. There is even a few Caravan touring sites about 25 mins out of the city.
https://www.donthibernate.co.uk/liverpool/
This is on the outskirts of a large village opposite a pub, its 20 -30 minutes in to the city centre but in a nice rural location.
https://www.bridgefarmrainford.co.uk/campsite

Pub opposite
https://junctionpubrainford.co.uk

There is a station but its on the wrong line for the city centre and would need a change.

You could take the caravan to Edinburgh! There's a caravan club site at Silverknowes, it's a bit off the beaten track but there's a bus route just along the road that takes you into the city centre. Or Moreton Hall campsite on the south side of the city is probably in a nice location and similar bus journey.
Or I'd look at AirBnB apartments with kids that age then you can make your own breakfasts and lunches and aren't tied to eating out every night. There's a lot of free activities in both cities and public transport is very cheap around Edinburgh.