No, they divested themselves of the DNO part of the business around 10 years ago to UK Power Networks, who are owned by the Chinese.
The DNOs in the UK are at the moment struggling more with managing a large increase in microgeneration than they are coping with rising demand for EVs. In the old days it was easy: all the demand in a distribution network came from domestic and commercial businesses, whilst all the supply came from the National Grid via the high voltage Transmission Network. It was relatively easy to balance the two at Grid Supply Point (GSP level) - effectively metering it at the substations that convert the high voltage Grid to the 240V distribution network.
Now what's happening is that there are loads of people creating small volumes of electricity directly on the network at 240V, so much so that the DNOs are having to cap the amount that can be exported back onto the 240V network across your MPAN/supply point - currently it's 3.8Kw, any more than that has to be spilled somehow as the network can't cope because once the high-voltage power has come off the grid into the distribution networks, it can't be put back up onto the Transmission Network. This also applies to the smaller solar farms that export at 240V, this is why there's so much demand for 2nd-life EV batteries to provide buffering and storage to extend the useful generation period of the solar and reduce the excess generation on the distribution network.
As more people switch to EVs this limit will be able to be raised as there will be more demand on the 240V network, but currently people are using battery, water heating, and electric thermal blocks to store their excess microgen capacity. So the DNOs are always happy when people install both solar PV arrays and EV batteries, it makes their life very easy - and of course like Rob and Shooter have reported, gives the owner effectively free motoring.