How far can jodrell bank look?

It's not a set distance.
The limit is determined by how much signal reaches
the antennae.
A powerful source can be 'seen' farther than a weak one.

The short answer is...As far as your telescope can see. Telescopes now in existence can reach almost to the edges of what is commonly believed to be the edge of the galaxy. (That's 13.7 light years, give or take.) This goes back to the Big Bang (if you believe in that) and may well be the limit of how far we can see as what is beyond the area of "normal" space is pure speculation. Some theoretical Physicists propose that there may be NOTHING there... (try getting your brain around that one!) All of this, of course, presupposes that Jodell Bank can look at all.

Let me answer your question this way. You can have a huge telescope, but if the image is faint, it will be difficult/ impossible to see. You can have an object that is lightyears distant, but is very bright.