Tube is cheapest and pretty easy but feels slow - Piccadilly Line to Green Park then change to Jubilee Line to Southwark. £5.30 each.

Next up price-wise you could do Elizabeth Line to Farringdon and change to Thameslink 2 stops down to Blackfriars. That would be my preference. Sit at the very rear of the EL train and you’re prime position for the lift (elevator) at Farringdon which takes you straight up to the Thameslink platform. You’re then at the front of the Thameslink train which is the end you want to be at to get off at the south side of Blackfriars station, for the short walk to the hotel. £13.30 each. Note - on a Saturday it’s off-peak so any further travel that day on TfL services would be capped at just a couple of pounds more than the single fare, so this is a good value option.

You would struggle to get an Uber for £35 and it will take ages in traffic. But if you have a lot of luggage and don’t like carting it around, it’s an option.