There is no proof of this evidence on the DVLA website or in the correspondence sent to me, however I cannot deny that the vehicle had ran out of tax. Unfortunately I forgot to SORN the car over winter.
You clearly know the binary options: tax or SORN.
You did neither.
Their proof is that a certificate of destruction hasn't been raised, therefore the car exists, and this VRM is neither taxed nor SORN'd.
IMO, it's this simple in principle and confirmed on the DVLA website:
Being the registered keeper of an untaxed vehicle. This is identified from DVLA records
But what is your intention, to tax(so that you can go to shows etc) or SORN?
IMO, all that could be at issue is the amount of the penalty.
Where's their letter?