Tele bridge pickup issue

[McCreed]

I’ve just started building a tele and when I sit the bridge plate in it doesn’t quite fit. I had to chisel out the bridge pup hole a little and that helped.

Did you check your scale length before your chiselled out the route?

It looks as though the hole that the pup wires enter into is too high so the wires seem to stop the pup from entering the hole. Should I attempt to drill out the hole and get the wires to sit lower?

I've seen this before, and yes, you can expand the opening so the pickup leads are closer to the floor of the route.
This can done a number of ways since you don't necessarily need to drill out the entire length of the hole. It just needs to be far enough in that the lead sits further down.
You can do it with a rotary tool (eg: a dremel) and a bit or sanding drum; you can use a drill with a bit larger than the existing hole; or you can even do it with a chisel. Which ever method, you want to take your time, be conscious of your working angle and ensure you don't go too deep and risk going through the back.

If using an electric drill, place a bit of cardboard on the top at the opposite end of the pickup route so when you angle the drill, the chuck doesn't rub up against the edge of the route. It will spin a groove into the edge very quickly. This may or may not be an issue for your finishing plans, but it's worth mentioning.

EDIT TO ADD:
It's best to keep these kind posts all in your Build Diary. It's easier for you to reference in the future, and easier for members to help you rather than bouncing between threads.