As the PM of a member nation of the Five Eyes, I'm pretty sure he's keenly aware of the mass surveillance done on the Internet traffic of everybody (even of that from nations referred to as "allies") routed through nodes controlled by Five Eyes member nations and the uses of that info for industrial espionage and political interference.
When setting up his sovereign internet network might want to bypass the UK too, by the way, given that as the Snowden Revelations showed they were some of the worst at this and already back then used their control of the end-points of most Atlantic underwater cables connecting Europe to North America, to do massive amounts of surveillance on Internet traffic between Europe to North America and then gave tons of that info to the US.
Including Britain in this network would just be a two-step way of giving the info to the US rather than direct.