Have hotel reservations on all 3 areas. First trip to London 4 nights 9/15-9/19, over a long weekend. Want to see usual top 5 -6 sights, tower Westminster abbey St. Paul, v&a, tower, British museum.
Two in Cromwell/earls Ct. tube stop, area, park city grand plaza and ash burn, staybridge suites vauxhall, apex Westminster
While I have never stayed at either of your Cromwell area hotels, I am temporarily living a few blocks away and pass both on a regular basis.
The area is fine for both. (The Ashburn is slightly closer to the Gloucester Road tube station and closer to Cromwell road so it will be a little noisier.
I have stayed at the Staybridge Suites Vauxhall. It is a fairly new, modern hotel. The rooms are slightly larger than standard UK rooms and you do get a kitchen. The breakfast is good and they do have a laundry room with free use of the machines. The service is good. (Note, they have a coffee machine (Nespresso) in the room but if you want capsules for it after your first day, you have to pay for it. There is a free coffee machine for use all day in the breakfast area.)
The only downside, I felt, was a location. During the day it was fine. However, at night, the walk from the tube station to the hotel itself felt a big dodgy after turning off the embankment.
We stayed at the Crowne Plaza, Cromwell, in South Kensington, three times. We were there for up to two weeks each time. Last year we stayed at the Conrad (Hilton) St. James Park and were also very happy. We stayed there for 21 days. We used hotel points for some of the stays. We were very impressed with the south Kensington area. Our hotel was right across the street from the Gloucester tube station.