Hi Natz - Never done it personally, but a mate of mine did two years ago and got a right result.
He turned up at Gatwick (just him and his wife) and went to a cancellations desk, told the person that he didn't mind where he went and was ready to go immediately.
An hour later he was on a plane to Menorca and on arrival was allocated a 3 star hotel half board.
He went for two weeks and paid £150 for the two of them.
Don't know if you can still do this what with all the new security restrictions, but it might be worth phoning your local airport.
Although he had a result, I'm sure that you could end up in a really grotty hotel, so might not be advisable if you are going with kids.
Another way is to go to the local TA a couple of days beforehand, and see what 'allocation on arrival' deals they have got. You can usually specify where you want to go and the minimum standard of accomodation.