Gatwick airport to London

Pay by contactless card after 9.30am weekday, any time weekends and it is £10.70 each on any train other than the Gatwick express.

who was giving out Gatwick-London fares in euros????

The answer really depends on where in the massive city of nearly 9 million people you need to be. But it will almost certainly involve the above advice.

One thing to note is that any form of road transport will be tortuous - there is no quick road route into the city. the train will be much quicker, but which route to take depends on exactly where you want to get to.

We rode the train from Gatwick to London. They did have a fast train which made no local stops. We enjoyed looking in everyone's back garden along the way. P.S. We did take the cheaper local.

The "fast train with no stops" is NOT the one you want to get. That is the Gatwick Express to Victoria, which is very expensive and only a few minutes quicker than the standard Southern trains. In any event you might well want to take a Thameslink train which goes through central London passing through London Bridge, Blackfriars, City Thameslink, Farringdon and St Pancras.

Taxi, even split between four, would still be way more expensive than the train. Where do you need to go in London? Trains go to Victoria Statiion or London Bridge. Victoria is a traffic hub offering good tube and bus service across the city. London Bridge probably less so, but good if you are staying near the Tower for example.

With trains every 15 minutes or so, there is no waiting, unlike the bus, where unless there has been a change in the past few years, where you wait in the open air, on a sidewalk walk with no, or little seating.

Thank you for everyone's input. We will be taking the train from the airport to Vauxhall which is the closest stop to our hotel in Westminster. We will then split a cab versus walking 20 minutes or trying to cram on a bus with baggage.

If you change off a Victoria bound train at Clapham Junction you can get a main line train to Vauxhall (Waterloo bound).
That is £10.50 contactless, so just a bit less than a London terminal station.
Clapham Junction to Vauxhall is every few minutes.

Vauxhall which is the closest stop to our hotel in Westminster

I can't think of anyplace in Westminster where Vauxhall would be your closest station (because its across the river and Pimlico - on the Westminster side - is the next station. Perhaps Vauxhall might your closest NATIONAL RAIL station.

So I would just take the Southern train all the way to Victoria, then double back one stop on the Victoria line to Pimlico.