Southampton University Aviation Society own their own aircraft & can train for the NPPL(A) SSEA at Popham. Even including the Society's membership fee (£120 pa) & the airfield's membership fee (£170 pa) training at £40 per hour will be much cheaper tham anywhere else, although I'm not sure if that includes instructor fees.
The NPPL is a UK only licence but the CAA are working towards an upgrade path to a full PPL. The information on the Aviation Society's website that says that the NPPL limits pilots to certain categories of aircraft is outdated. An NPPL(A) holder with SSEA can fly Cessnas, Pipers & most of the common single engined aircraft.