This opens up a lot more doors. For example the British Autotest Championship is within your grasp, inlcudiong the cost of an Autotest ‘Special’ at around £1000. Don't forget that you will need a trailer to get it to and from events, though.
Sprints and Hill Climbs also come into this budget as there are categories for standard road cars and lightly modified road-going road cars. Entry fees are around £85 per event and you will also need a Competition Licence and Motorsport UK compliant helmet and fireproof overalls.
Karting also falls within this budget; a complete, ready-to-race kart and spares can be bought second-hand for between £1000 and £2500. Again, you will need a trailer to get it to the meetings.
As an alternative to driving, this budget will allow you to compete in one of the many stage rally championships as a co-driver. Your main cost is a contribution to the entry fee, and for many events, you will need to buy a set of the organisers’ route notes. An average forest rally entry fee is around £500 per event, and route notes are in the region of £30 per rally. Your other costs include petrol to and from the event, and local hotel accommodation.
You could start circuit racing, for example with 750 Motor Club’s Stock Hatch and MR2 Championships, while on the drag racing front you have the budget to buy a second-hand drag racer for the Pro E.T. series, which will entail tearing down the strip in around 10 seconds.