It’s a pain, but definitely worth doing it legit as the potential consequences of building over without approval are really bad.
We had to bridge a public foul sewer on both sides of our extension, application cost was ~£400 (I think), survey costs before / after came to around £600, and Severn Trent insisted we repair a short section just inside the footprint of the extension. It was in a bad enough state to need repairing, but not bad enough that they would do it :o/ We replaced the entire run in the end, but that only added an extra £750 to the bill as the builder managed the contractors / timing very well to minimize costs.
The storm drain (3m deep) that ran parallel to the extension was another matter entirely, and caused a whole load of problems and expense.
We found that Severn Trent were very conservative when it comes to anything other than strip foundations, although the guy we dealt with was really helpful and worked directly with our builder + building control to come up with a satisfactory design.