Ride services

If your hotel is in central London, then the easiest is to just get a taxi. It can't be very far.

Uber is also available.

Agreed - just take a taxi from the rank, no need for a ride service.

Depending on where exactly it is the tube or walking may be better. Is a “ride service” a taxi?

In general the best "ride service" in Central London is the tube, but the actual answer depends on exactly where you want to go.

The OP is not exactly clear on what they are looking for and I'd usually be one to immediately consider the tube/walking or a taxi, but I get the impression that the OP may be looking for a little more. Maybe a car service in which the driver meets the clients and helps with luggage? That is what comes to mind when I read "ride service". This might be a family group and the OP has indicated difficulty with stairs --

https://community.ricksteves.com/travel-forum/england/avoiding-stairs-at-tube-and-train-stations-in-london
https://community.ricksteves.com/travel-forum/england/hotel-near-heathrow-easy-to-access-for-old-folks-like-me

Thanks, everyone, especially Virginia who tried to figure out my request by researching my other posts. Yes, we are family of 5 including 2 grandparents. We've always used the tube, but I can't really do it anymore with luggage. We are staying in Covent Garden. Sounds like you all recommend a regular taxi. I think we will go that way.

If I remember correctly the taxi rank is on Pancras Rd., which is the road that runs between Kings Cross and St Pancras Stations, near to the Great Northern Hotel.

it was a few weeks ago, well signed