We had a similar situation, 30’s semi, extension on hill, proximity to storm drain (3m deep).
We were advised by a structural engineer to go with piling and commissioned foundation designs accordingly – Severn Trent said no, they are very wary when it comes to unconventional foundations.
After working with building control, a different engineer, and our builder we specced deep trench foundations which were acceptable to Severn Trent, and much cheaper than the piles. Still bloody expensive, mind.