Up until the early twentieth century, Luton was a village in the countryside between Chatham and Hempstead. There was a pub (the Hen and Chicks, which is still open), a church and a few houses. People from Chatham used to go on holiday to Luton and to Hale a little further along the road. The Waggon at Hale (another pub which is still open) offered rooms for travellers.
As the dockyard expanded, houses were built along the road to Luton, and it wasn't long before Chatham and Luton were joined permanently.
Luton sits between Chatham Hill and the All Saints area (where the Medway Union Workhouse was).