If you want to use a taxi, set the pick up destination as per 24s but use Addison Lee. They're some way between Uber & Taxi in terms of cost but super reliable, can be booked in advance & will do it as a fixed fare. They should get you across London at 11am on a Sunday morning in under an hour.
Alternatively, try and get he 1122 from Vauxhall and if you miss it, get a cab from there. That will mean you skip the heavy traffic parts