Northamptonshire has CountyConnect, which covers most of the south, west and north of the county with four 'service areas': Brackley/Towcester, Brackley/Banbury (includes a few villages in Oxfordshire), Daventry, and Welland Valley (service aimed at Market Harborough, actually in Leicestershire). The north-east of the county is tied in with Lincolnshire's CallConnect.
You have to register, and pre-book at least one hour in advance.
Having seen the minibuses in Daventry town centre, they seem well-used from there at least, although given the need to register etc., I suspect everyone is local and regular.
It's likely the service will be scrapped in September 2018 as part of the County Council removing all bus service subsidies (they have huge financial problems and have basically run out of cash).