Max line speed of HS2 is 360km/h, with provision for 400 in some sections in future. This is entirely in line with many other modern HS lines. China’s been running regular 360km/h services for years.
This is a project with a 200+ year shelf life. Designing to 300 or less would have been short sighted, and many of the changes to accommodate such high speeds actually reduce costs in the long term (slab track, headroom to catch up delayed services, ability for one trainset to operate more services per day etc).
The cost overruns of HS2 are primarily from plain old poor project management, complex planning law and constant political meddling, not engineering decisions.