You're not the first person to have these kind of issues, the DVLA are experiencing severe delays due to the coronavirus lockdown over the last few months. We can't say accurately whether or not you can drive legally if the DVLA itself can't give you a straight answer, but I'd look at Section 88. That would potentially allow you to keep driving even when the DVLA is processing your application, but I believe it applies to people who've sent in an expiring licence to be processed and they haven't yet got a physical copy of the renewed licence: assets.publishing.service.gov.uk/government/upload...f