there's the novelty of the docklands light railway, and the little trundle train at Stanstead, but none of the main lines or the underground are autonomous.
The Victoria line has been fully autonomous since 1968, the Central Line since 1995, the Jubilee since about 2005 and the Northern since this year.
The "driver" has to close the doors because automated systems are not able to very that all passengers are safely clear. Otherwise everything is automatic. The door problem has been partially solved on the Jubilee line by fitting platform doors aligned with those of the train.
It's that sort of 'cleaning up' of the environment that has to be provided for an automated system to work. Very expensive but with the added benefit of a massive safety increase.