Looking to outsource some CNC routing in UK

[Ger21]

Do you know anything about the technicalities of CNC routing? How to get the prices down or how to design MDF components so they are quicker to cut?

Without knowing exactly what you're doing, it's difficult to give recommendations. Every job is potentially different, and can present it's own challenges.
The big difference in pricing you may be seeing may just be due to the fact that some people don't know what they're doing, or how much they should be charging (at the low end). The high prioces may hjsut mean they don't want your business. I'd go with the cheapest one, and see how they're quality is. If they don't work out for you, go to the next cheapest.

I've been programming routers in custom cabinet shops for nearly 20 years. If you want to send me your design, I may be able to give you some ideas.