Morning mbga9pf,
The next door neighbour did something similar last year. A 50m long dig from house to a ditch at bottom of garden to discharge rainwater (not as many junctions but a similar length).
So I had hired a mini digger for a week to put a retaining wall in for same ditch, cost me around £300 all in. Just go round your local builder's merchants, plenty have plant to hire. If you need insurance then that can be bought at a price for the week.
Lent it to neighbour for the day while I was pouring concrete. His learning curve was around an hour then he was digging trenches. The hardest part was getting the fall right but he cracked it in the day.
He then laid the pipes the next day (prices are available on the internet, my guess is that noseall has included his markup - nothing wrong with that of course, but you don't need to pay it). He had to cover it all up with a spade and some manual labour but there was no rush.
He didn't do the pressure test and pea gravel thing, maybe you should, but it's only rainwater. You can call building control and I am sure they are very friendly, they weren't interested in my neighbour's job. If it was me, for rainwater I wouldn't bother them, could open a can of worms.
If you want somebody to dig the thing for you then ebay is full of lads selling a business card for 99p and you get the digger/man combo for whatever they charge. Round these parts you might only pay £140 + delivery a day. My neighbour did it in a single long summer's day and he was a amateur hack.
Obviously whatever you price it at to DIY will be less that the final cost but £4500 would be a nice little earner for a builder. They are, of course, in the job to make a profit.
As for a price per metre. I seem to remember reading in a self build 'bible' (2008???) that it works out at about £40 a metre. Material prices will have gone up since then, labour charges should have dropped. That will be for foul drainage done properly.
Just a guess.
4500?!?!