Just as an update in case anyone else comes across this problem, I've had a response from the DVLA after disputing this fine and they've agreed that no further action will be taken.

The person on the phone said it had been sent back undelivered, and that someone at the address must have sent it back with a note that I didn't live there. I definitely did live there, alone, and I definitely didn't send it back. Same address they sent the fine to so they must know I live here! They also made me pay £25 for another V5 so I could tax the car

Hi, Just after some advice about whether it's worth me disputing this fine or whether it's entirely my own fault! Paid my car tax by direct debit for the last two years. Last year I moved house, sent off my V5 change of address to DVLA and thought no more about it. This week I received a penalty notice stating my car hadn't been taxed since March 1st - news to me! I called the DVLA and it turns out my new V5 was returned to the DVLA last year as 'undelivered' and I had never noticed it hadn't arrived. Apparently this meant my direct debit wasn't renewed for the year and so my car was left untaxed. Could I have expected the DVLA to have been in touch at any point, either to say my V5 had been sent back, my dd wasn't renewing or my tax had expired? Without checking my dd has left the bank every month I'm not sure how else I'm meant to have known, and I'm annoyed at having to pay a fine! Is it my own fault for not noticing the V5 hadn't shown up?