Yes, with pervasive CCTVs, porn filters, and Five Eyes, the UK has arguably lost your trust and you feel company X (google in your case) more closely aligns with your values, but you must realize that this corporatism is corrosive to democracy.
The government is you in proxy. You can vote out the government. You can sue it in court. You can blog about its abuses. You ARE the government.
And yet, here you are saying that you want some private company which does business with and operates under the jurisdiction of the government to receive and retain all your private data.
This company has no loyalty to you. Your interests are seldom in perfect alignment with its interests. Unless securing your data serves their business interests, they will not fight back if the UK government asks for your data.
You are introducing indirection in your interactions with your own duly elected government and that is going to cost you your voice in the direction the UK is headed.
My problem is that in my specific case, I can't. I lived here for 8 years but because I don't have a British passport, I cannot vote this government out. The government here does not represent me or care about me - so the only way I can take care of my own future is by voting with my wallet - and I would rather trust google with my data than the UK government. I do see your general point though.