Between Paddington and Heathrow the European Train Control System (ECTS); west of Heathrow and east of Stratford a legacy system is used; and the central section uses a modern signalling system from Siemens.
Seems like ETCS couldn’t do automated train operation (ATO) back when the tenders were going out, so they commissioned Siemens to deliver their proven Trainguard CBTC system for the core. Since then, systems like Thameslink have used ATO on top of ETCS Level 2, but that’s still a fixed block system so probably couldn’t do enough trains per hour for Crossrail. ETCS Level 3 can do moving-block, but I don’t think there are any ETCS Level 3 implementations anywhere in the world yet.
I believe the way that they operate is that the train is driven by the driver through the ETCS and older TPWS signalled areas, and then when it goes into the core the train switches over to automatic control.