There’s going to be a lot of ‘normal ‘ people on the tubes at the moment and police and army/navy personnel to guide people around due to the Queen’s funeral and associated events. That said I’d avoid changing at Green Park as this is subject to last minute cancellations and one way systems for crowd control reasons.

As others have said Elizabeth Line or HEX to Paddington then Elizabeth Line to Canary Wharf where you can jump in a local cab or take the DLR to Island Gardens.

Citymapper is suggesting Uber all the way would be around £55. Depending on the route not sure if that would increase most of central London was a car park today with longer journey times and lots of tourists…

You could always ask ground crew f they can give you a taxi on account all the way citing safety and if you’d been rebooked to LCY BAs duty of care would have been for a couple of hotel nights and see what they say. Remember though ground staff would have lots of irrops so would be tired and stressed.

Travel safely and let us know what you do.