Hi, I work on web in London. The prestige of the company isn't as important as having proved you can work and learn. In fact you should probably ask that on interviews - what will you team be like and what kind of opportunities will you have to learn and grow as a dev? It's never good for a dev to work alone, but it's especially harmful for junior devs.

I don't know the market for Haskell. If you want to get into backend for web, you can't go wrong with Node.js. Agencies using those services usually prefer the backend written in Javascript or Typescript so more devs can, in principle, work on both ends. Moreover, you can get into cloud services like AWS and Azure easily if you know Node. I reckon it will be easier to start as generic "web developer" or "junior developer" and then gradually evolve into backend. Specialists tend to be mid to senior.

You should start sending applications on your last month. I don't think it will take you more than that to land a junior role in London (there are many more junior openings than internships). But you can create a Linkedin account today if you don't have one.