Seems unlikely. I've seen teams at GDS + teams based on the GDS way of working in other UK gov departments solve some really knarly problems.
The companies who capitalised on this (Kainos/Equal Experts/ScrumConnect) are now their own oligopoly.
It's just big guys charging arms/legs for average work again.
Look for yourself, GDS is hiring a "Lead Technical Architect" for £67,126–£91,453 https://gds.blog.gov.uk/jobs/ . FAANG (and Palantir) pays up to triple that. How can GDS compete for talent?