Check out the Yamaha TRBX basses. The 304 runs at about £250 which would leave you with a decent budget for the rest of your gear (amp, effects etc.)
They're light, have a huge sound with lots of variety. You get a 2 band EQ to boost or cut the bass and treble, and a 5-way switch that offers up another 5 pre-set tones.
My experience with Yamaha gear is excellent, particularly when it comes to the quality control and factory set up. I don't think anyone else offers the same quality at this price point.
http://uk.yamaha.com/en/products/musical-instruments/guitars-basses/el-basses/trbx/trbx304/?mode=model&vmode=pc
http://www.gak.co.uk/en/yamaha-trbx304-4-string-bass-car/81931