Have a look at the OS map - Lasham is most certainly on a hill. Altitude is 182m. Odiham is 121m, Popham is 157, Basingstoke station is 95 and Alton Station is 101m.
Well I suppose it depends on your definition of a hill. Not exactly what I would call a hill site, but then as a glider pilot I would have said a hill site was one with a soarable ridge. I used to cycle there from Basingstoke, and it wasn't exactly hard work. Now what I would call a hill site is the Long Mynd, or maybe the Montagne Noir. Shall we say gently rolling countryside and leave it at that?