The gov website is not indicating any delays or closures that affect licence renewals from what I can see.
You can apply by post by getting a D1 pack from a post office.
It says for a post application you only need identity documents (passport) if you’ve changed your name.
Only hurdle is you need to send a suitable passport photo.
Apply by post
Order a ‘D1 pack’ of forms from DVLA or get one from a Post Office that deals with DVLA photocard renewal or vehicle tax.
You need to include these things with your completed forms:
a recent passport type photo (do not sign the back of the photo)
your current photocard licence, if you have it
a cheque or postal order for £17, payable to DVLA (no fee is needed if you have a medical short period licence or you’re aged 70 or over)
You also need to include identity documents if you’ve changed your name.
Send the application to:
DVLA
Swansea
SA99 1DH