DVLA do not give first 7 days to renew your road tax. And Lutz I believe to be wrong with the advice he is giving.
When I had a UK registered car in France I was told that I had to be insured and taxed in the UK or re register in France, the car had to be legal on UK roads at all time.
My daughter and son in-law were told the same when they moved to France last year. My son in-law kept his Mercs until end of year was coming up and sold them back in the UK and now they have French registerd cars.
Advice to Brits who move between UK and homes in Spain is that a car has to be taxed and insured and MOT'd (if required) in the UK or be re registered etc in Spain.
Advice from PLND (police national legal data base)
"Question Q370
Have I got 14 days grace to get my new tax disc when it runs out?
Answer
No, however there is an exemption for the first 5 working days of the month from displaying a valid tax disc. The exemption will only apply in the month when the tax disc commences and where an application for a new tax disc has been made before the old one expires. Drivers should continue to display the previous tax disc until the new one arrives. After 5 days the offence will be committed if the new tax disc is not displayed.
You have advance warning when the tax is due to expire, either six months or twelve months. You should make arrangements to re tax your car within plenty of time of the expiration date of your current tax disc. You can tax your vehicle on line, see website in related information for more details.
Irrespective of whether a car is used on a road the DVLA send out automatic penalty notices to anyone who has not renewed their tax disc (unless they have completed a Statutory Off Road Notice). However, the DVLA delay sending out such notices until 14 days after the licence is expired, which is where the myth that there is 14 days grace probably began."
Finally - From DVLA with URL below
"Vehicle tax due to expire while you're abroad,
If you're going to be abroad when your vehicle tax expires, you can tax online, by phone, tax in advance or get someone to tax your vehicle for you. You can arrange to get the tax disc sent to an address abroad.
Tax in advance
You can renew your tax up to two calendar months in advance in person or by post at a Post Office