If you move, the law says you must update your vechicle log book V5. Failiure to do so could result in a £1000 fine (seems OTT imo). Anyhow its always been pain because the DVLA can take months to send it back and sometimes they lose your documents completely. You'll need your vehicle registration number, log book document reference number and postcode to use the online service, which can be accessed on the DVLA website. https://www.gov.uk/change-address-v5c Once completed, you can expect (hope) to recieve updated documents in 5 days. But if you don't at least you still have the previous one...
Its all much better with the online system now. I attached a new private reg to my daughters car. It took just two minutes to sort. Nothing to post, all we have to wait for is the new log book to return. Any system that avoids snail mail, or worse, dealing on a telephone with the idiots down there is a massive improvement
Sounds like genuine progress in simplifying a routine task. Be nice if they extend it to things like registering your bike/car as an historic vehicle instead of form filling and posting it all off to be lost or ignored.
Just done all mine very quick and simple. Did my driving licence as well which takes a bit longer and requires more info. I didn't realise my licence ran out last month so had to cough up the £14.00 renewal fee.