Wash the mussels under cold running water and discard any that are open or don't shut when tapped. Pull off any fibrous 'beards' and remove any barnacles, then rinse again.
Heat the butter in a large saucepan, add the garlic and cook gently for 1 minute. Tip in the mussels and add the cider. Bring to the boil, then cover and cook for 3–4 minutes, shaking the pan occasionally until the mussels have opened.
Using a slotted spoon, transfer the mussels to 2 warm serving bowls, discarding any that remain closed. Reheat the pan juices, add the cream and thyme and season. Pour over the mussels and serve with plenty of crusty bread.