You say on your other thread that your husband is not comfortable with Air BnB or VRBO type lodging. But what about a serviced apartment in an apartment hotel? These provide the services and security of a hotel (reception desk, lobby area, maybe a fitness room, and others), with apartments instead of individual bedrooms. There are a number of “chains” that offer good options in various London locations.
For 5 adults, Marlin Apartments offers a 2-bedroom apartment ( 2 king beds) with sofa bed in the living room for £450 a night. If that is not enough beds, you could get the 2-bdr and a 1 -bdr or studio in the same building.
https://www.marlin.com/
Other Marlin locations offer different options. Waterloo is a good location.
Cove Cannon Street offers nice modern apartments between St. Paul’s and the Tower of London. 2 one-bedroom apartments would be around £700 in May.
https://www.staycove.com/en/london/cannon-street-apartments
Other companies to try are Citadines, Native, Staycity.