Most policies will only allow you to drive cars you DON'T own third party - otherwise everyone would be insuring a really old group 1 car and running round in much more powerful cars on the third party bit! Also some policies state the other vehicle must be insured in its own right for the third party bit to be valid.
You could get your current car HPI checked and get the 7-day drive-away insurance to cover you (at £30 for 3 checks it's probably the cheapest way to get very short term insurance!) More details at http://hpicheck.com/driveaway.html
Have no fear, Audi have it covered! When you buy a car from an Audi dealer, they will issue you with a phone number to call for Audi Insurance. Phone this number quoting the centre number and chassis number of your new car and Audi Insurance will give you 7 days free full comprensive insurance (also covers over drivers if needed). Your centre won't have mentioned this to you yet as this cannot be done until the car is physically in the country. This should give you the time you need.
I can never work it out, sometimes Audi Insurance are very competitive, other times they quote crazy amounts -if they don't want to insure me just say! They quoted me £650 on my impreza (colin special edition) and yet £1800+ on my old VW Sharan!
Let's face it, the quote is worth hearing just to get the 7 day cover note!