Calais to Eymoutiers takes between 7 and 8 hours by car. Head south to Rouen, then on to Chartres, Orléans and Limoges. At Limoges, come off the A20 at junction 35. Follow signs for Eymoutiers. Ideally situated for a stop-off on your way south through France.
Depending on the time of year there are daily flights to Limoges with RyanAir from Stanstead, 3 times a week from Manchester and up to 4 times a week from East Midlands airport. Flights between May and September are available from Bristol and Leeds/Bradford airports.
Flybe fly to Limoges from Southampton 3 times a week. They also have seasonal flights from Newcastle and Birmingham
Cars can be hired from Limoges airport. Alternatively, you can take a taxi to the train station and get a train to Eymoutiers. Once in Eymoutiers there is no onwards public transport for discovering the area so a car is highly recommended.
Take the Eurostar from London to Paris. Trains from Paris to Limoges take just 3 hours, from where you can get a train to Eymoutiers, taking 45 minutes. Once a day there is a TGV Limoges - Lille, so you can avoid changing stations in Paris.