You can get a new clone of a Honda GX series engine on ebay for less that £100.
1 x Petrol Engine. Engine Type: Force-Air Cooled, 4 Stroke, OHV Single Cylinder. Bore & Stroke: 68x45mm. Engine rotation: Anti clockwise. Easy to start, smooth running with minimal vibration. 3.6L fuel tank, threaded oil tank cover, NBR gasket below the tank to prevent vibration from damaging...
www.ebay.co.uk
Rig up a base for the setup and run a small three terminal alternator with a belt drive and a big pulley on the engine, and use a 12V deep cycle / leisure battery for the power storage.
Even at eg. 100A at 15V from the alternator, that would only be 1500W or around 2hp; the engine would running at quite light load.
I've worked on one of those engines, they are pretty good, with an easy-starting system.