NorthHampton drives me mad too - I've lived here quite a few years now, and I'm sure this pronunciation has become much more common in recent years.
Not long ago, I looked at several online dictionaries to see what pronunciation was given, but of all the ones I looked at, only the BBC dictionary gave NorthHampton. That explains why their presenters are the biggest offenders!
All the older people I know here (over 60) pronounce it without the H. They tend to be the ones who have quite a pronounced regional accent, and to be honest I think that the accent makes it almost impossible to put an H in the middle. For that reason, I am tempted to think that NorthAmpton is the traditional pronunciation. Younger people, on the other hand, don't tend to have the same accent, allowing the superfluous H to creep in. Hypercorrection, maybe! That's purely my personal theory, of course - I've no proof whatsoever to back it up.