Brittany Ferries has an overnight crossing from Portsmouth to St. Malo (Dep 8pm, Arr 7.30am next day). It is approximately 4 hours by car from St. Malo to the Logis.
Ferry between Caen and Portsmouth (4 per day). Approx 6 hour drive to Caen.
Car hire available from Poitiers or La Rochelle. 

Eurostar from London to Lille. From Lille the TGV to Poitiers. From Poitiers, local train to Mauze sur Mignon Or London to Gare de Lyons, Paris. TGV from Gare Montparnasse to Surgeres (15 mins by road from the Logis). Some trains also stop at Mauze sur le Mignon 

RyanAir from Stanstead to La Rochelle (approx 30 mins by road from the Logis)
Or from Stanstead to Poitiers (approx 1 hour by road from the Logis)
FlyBe from Southampton to La Rochelle
Or from Birmingham to La Rochelle
EasyJet from Bristol to La Rochelle and Bordeaux (approx 2 hours by road from the Logis)