From Gatwick to the British Museum area

If the hotel is east or north of the British Museum, take the Thameslink trains to Farringdon which is about a mile east of the British Museum or St Pancras which is about a mile north of the British Museum, whichever is closest and take a taxi if too far to walk.

If the hotel is over a mile south or west of the British Museum then a train to Victoria Station makes the most sense. Thameslink trains are a lot less bother than going to Victoria station and then taking underground train(s).

From Gatwick, the Southern Railway Train or the Gatwick Express Train will take you to Victoria Station.
From Victoria Station, the London Tube’s Victoria Line goes to the Oxford Circus Station from where you can transfer to go one more stop to reach the Tottenham Court Road station— the closest tube station to the British Museum

You can pop in your details to TFL’s trip planner

https://tfl.gov.uk/

If you need to go to Victoria station there are 2 options. The Gatwick express and southern trains. The southern trains take a little longer and stop along the way but are cheaper.

Realizing now that the new Elizabeth line means direct train access to Tottenham Court Road via Farringdon. So Thameslink trains to Farringdon, and then Elizabeth Line one stop west to Tottenham Court Road, all on one rail ticket. No need to juggle the underground, or a second ticket specially for that. The whole journey is likely stairs-free. Be ready for the view from Blackfriars bridge over the Thames.

The step free option sounds nice. But hopefully the op’s hotel lies along the Elizabeth line.

As for tickets there may not be a need for any at all. I paid for my trips to and from Gatwick using an Oyster card. Contactless credit cards and smartphones and some watches may be used too. Use the same method to tap in and out. Counts toward the daily cap as long as you continue to use the same payment method.

Thank you every one for your help😊

Just a handy reminder for anyone using the TfL trip planner when you’re not in the U.K. to keep time zones in mind while researching. You can get some weird results if you’re looking at night in the USA and it’s like 3 am in the U.K.