We were in London in May 2018 (would love to go back). We had 5 days there, and it wasn't enough.
It is expensive to do just about everything, but that was expected. We budgeted for it, and probably blew the budget.
The best value thing in our opinion though was the accommodation. We stayed in the Travelodge in Covent Garden (Drury Lane). From memory for the 5 nights we were there, it was around $700 (NZ), including breakfasts (that was for a queen room, pretty basic but it did the job nicely).
From Covent Garden you're. close to the Tube, smack bang in the middle of the West-End, really close to the theaters and walking distance to the river and Leicester Square.
Paris, the same - we lucked out on a really central AirBnB in the Latin Quarter with a view down the street to the Eiffel tower. We were there 4 nights, needed another 4 I reckon.
Have you asked the kids about Disney? They may be of the age they'd rather actually see a real city than a made up one? I only ask this as we took the kids, then 9 and 10, to Canada (therefore via the US) back in 2002 and gave them the choice of Disney in LA on the way home, or a weekend in New York. They both chose New York, and they still talk about it today.


