Yes, EIS allow you to use their indoor track for something like £3.
They don't make it very clear that the public can access it on the website, they probably don't want to encourage too many turning up en masse.
I used it a couple of weeks ago - being a bit slow I was often in the way of the elites which was a bit awkward but they seemed to tolerate me (they shout TRACK! if they're coming up behind you).
There's Don Valley Stadium as well, but a bit cold in this weather (not sure if its open in the winter, but certainly in the summer).