Cheapest transport methods from Oxford to London?

There certainly are!

The Oxford Tube bus is £18 return, or £14 if you're over 16 and under 26. Megabus is £9 or £10 depending on the time of day. The cheapest I can find by train is £25.- that's the standard off-peak fare.

When in London, the way to get around is use an Oystercard, or your contactless bank card if you have one. Get an Oystercard from any Underground ticket machine and it will be £5 for the card, plus £6.50 to go anywhere in Zones 1-2 for the day. These are the only Zones you're likely to want. The way it works is that the fare on the tube will be £2.80 and it deducts that from what you have on the card each time you travel, but there is a daily fare cap and once you hit £6.50, you don't get charged any more. This also works on London buses - £1.50 flat fare on any bus however far you go.

The £5 is a refundable deposit so you can give the card back at the end of the day and get your deposit back plus any more money still on the card. Or keep the card for going to London again, and you won't have to pay that again because you already have the card.

Or if you have a contactless debit or credit card, that works exactly the same as Oyster, prices are the same including the daily cap, so you don't even have to pay a deposit or fiddle about with ticket machines.

The one thing NOT to do is buy a one day Travelcard. This is £12.10 and it's deliberately extortionate compared with Oyster or contactless to encourage you to pay electronically! TfL's ultimate aim is to get rid of paper tickets - I don't suppose it will ever get there entirely, but it's already achieved closing all ticket offices now that the machines can do everything.

Get the 'Oxford Tube' - a bus from Oxford to London. £18 return for adults, £14 for young person

When you're in London; get an Oystercard (top-up card you can use anywhere on London transport - tube / bus / overground, automatically caps at £6.50 a day), or a travelcard (paper ticket, £6.40 for zones 1-2) - you can also use a contactless bank card as an Oyster equivalent

I always do that journey by the Oxford Tube (a bus), but my son tells me the Megabus is cheaper. Get an Oyster card for London tubes and buses, as sunshine mel suggests.

Hire a private jet if you can't afford to buy one