Any decent Builder or Groundworker should be able to work out the levels and lay a drain accordingly. Most Drainage Co's are only interested in clearing blockages or repairing what's already there. (Often at extortionate prices!)
It's not a DIY job at the depths you're talking about, and any connection into the existing sewer needs to be made at the current invert level. Secondly any reputable contractor will have appropriate insurance, (although worth checking this for your own peace of mind), hit a buried service, and it is costly, hit a fibre optic cable and you'll need to win the lottery!
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