Airport Hotel at London Gatwick

Try googling. I just did and there are many.

"if there is a hotel at the Gatwick Airport in London? We need to stay in London" - Gatwick airport is not in London. It is well south of London, half way to the coast at Brighton.
Yes, there are lots of hotels at Gatwick, but don't google for "London" or it will confuse google. You will not be staying in London, you will be staying at an airport, don't expect to see an London sights during your stay.

There is a nice hotel, Corner House Hotel it’s only a few minutes from the airport. They offer transportation to and from the airport...the corner house.co.uk

Bloc, right next to the departure gate, cant get closer and good prices. My go too. But just google as there are loads and loads and loads....

We like Premier Inn. There are three at Gatwick; two north of the airport, one to the south.
https://www.premierinn.com/gb/en/hotels/england/west-sussex/crawley/london-gatwick-airport-south-london-road.html?cid=GLBC_GATGAT

Use the website to research the other two.
Any one of the three would suffice.

There are two hotels literally connected to the North terminal....the Sofitel and a Premier Inn. I've stayed at the Sofitel and it was fine. Next time I'll probably stay at the Premier Inn.

If your flight is at the South terminal there is a free shuttle train between terminals that only takes a few minutes.

There are several hotels at Gatwick Airport. I've stayed at both the Hilton and Sofitel this year. I prefer the Sofitel.

I also spent a night at the Gatwick Corner House which is in the pleasant small town of Horley just a few miles from the airport. They offered a package of room, breakfast and airport pick up and drop off which I thought was reasonable.
Since my layover was about 20 hours I enjoyed the more village atmosphere and the ability to walk around a peaceful place.
I later found out that there is a terrific historic pub a short walk from the guesthouse but I was home by then.
I would definitely stay there again.

A lot of the hotels advertised as "Gatwick Airport" are in towns around it and you need to take shuttles. If this is an issue, use the two mentioned above that are actually in the airport.

Plus The Hilton attached to the South Terminal albeit via the multistorey car park.