According to Dan Bloom of The Mirror, the DVSA have confirmed  that all driving lessons and driving tests are suspended for the foreseeable future in line with government Coronavirus lockdown rules:

Dan Bloom
Have just made a small correction to this piece – we’ve checked with DVSA who tell us driving lessons/tests will *not* be allowed under the new lockdown.


We expect the DVSA to make an official announcement and clarification later on Tuesday 5th January.
When they do we will keep you updated.