the Driver and Vehicle Licencing Agency are one company
the Late Licencing Penalty office are another company
even with a letter from the dvla stating that they are wrong, you really have to be a pian int he arse to get them off your back
they wanted to do me for not taxing a car i'd scraped 3 years earlier, and because i didn't have the letter stating it was done they were chasing me for late tax etc
"officially" they request that you need to contact them if you have not received a reply to any documentation you have sent to them after 4 weeks so that they can check the system and avoid any fines etc that can be lurking on the horizon
if you do this on line then a simple screen shot or copy of the confirmation email should stop any further harassment
having sent the paperwork off you should explain that you have fulfilled your obligation and you should not be held accountable for the post office losing the letter or their staff misplacing it
also, even if you have proof of postage or proof of delivery, they will claim that it doesn't count as it's not been inputed into the system and go back to their "4 weeks notification period" standard answer