However, one A-list couple has made their home off the beaten track, in a tiny village between Lavenham and Stowmarket.
Game of Thrones star Kit Harington and co-star and Downton Abbey actor Rose Leslie bought their 15th-century moated timber-framed thatched farmhouse – called Popples Farm – in the late 2010s.
Kit Harington has lived in Brettenham with his wife Rose Leslie for several years (Image: IAN WEST/PA)
The pair were apparently sold on the area by popstar Ed Sheeran, who has an estate near Framlingham and grew up in Suffolk.
Their house is in Brettenham, a village that was first recorded in the Domesday Book of 1086 and is home to just 321 people, according to the 2021 census.
Almost the entire area is a conservation area, complete with ancient woodlands such as Ram’s Wood and the rising River Brett, and as a pretty village it is a popular spot for people hiking or cycling around Suffolk.
There is a 14th-century Grade I-listed church, called St Mary the Virgin, which people visit for its unusual history.
The village is home to a 14th-century church called St Mary the Virgin (Image: Google)
The tower is built on the south side of the nave rather than the west end, and its base serves as the main entrance porch, making it one of only 14 churches in Suffolk built with this specific architectural layout.
The closest place to stop and get some essentials is Hitcham Post Office and Stores, a five-minute drive or a 50-minute walk, really cementing the village as a secluded spot for the celebrity couple to raise their two children away from the public eye.
Their closest celebrity neighbours (that we know of) are supermodel Claudia Schiffer and her husband, film director Matthew Vaughn.
The couple made Suffolk their family home 24 years ago after falling in love with Coldham Hall, an Elizabethan Tudor manor near Bury St Edmunds, during an impromptu walk.