I suggest you buy a motorcycle. A 125cc (I suggest Honda CBF125) is more than nimble enough to get you around traffic quickly. Only £10 (more or less) to fill the tank. And if you're worried about safety just pick up
this,
this,
this,
this, and maybe 2 of
these and you should be fine.
The total sum of everything might be more than twice your budget, but you'll get your money back via savings in fuel and maintenance.
Plus these type of bikes can survive a lot of beating, low-sides & minor crashes before they finally go to motorcycle-heaven, but you're getting insurance as well right?