There are many routes from Britain to Italy and vice versa. One of the most direct from Britain is through France to the east of Paris to Dijon and then through the Frejus tunnel into Italy.
From the UK, depending on the time you cross the channel you can reach the Burgundy area that night.
We recommend the Maison Chaudenay (http://www.maisonchaudenay.com/about_chaudenay.php) in the small village of Chaudenay. Chaudenay is l0 minutes by car from Beaune and all the famous southern Burgundy villages. Bruce and Anne Leonard own Maison Chaudenay and Bruce is an excellent guide to the area. They offer three very comfortable apartments and require a minimum stay of 2 nights but as it is in the heart of the premier cru wine district with food to match, that is not a hardship.
We usually make our second stay at Chambery - a lovely town in Haute Savoie - and only a short distance from the Frejus Tunnel.
Philip and Edith Lanthelme Tournier are owners of Les Suites de l'Hôtel Particulier De Sautet
6, rue Métropole, 73000 Chambéry
This is a B and B. It is an 17th/18th century building in the historic centre not far from the cathedral. The surroundings are tranquil and quiet and Edith and Philip are thoughtful and knowledgeable hosts. The rooms have been beautifully restored and are most comfortable. There are only three rooms to let. There are many good restaurants within 100 to 150 m. Breakfast is excellent.
http://www.booking.com/hotel/fr/de-sautet-les-suites.html?aid=312695;label=postbooking_confemail
The drive from Chambery to Il nido is about 9 hours by autostrada - a long day but bearable.