Which countries did the British Empire establish from the ground up?

You mean apart from Canada, New England (Now USA) Australia, Nigeria, Ghana, Gambia, (I'm doing all these from the top of my head I hope you are impressed lol) Sierra Leone, Kenya, Tanzania, South Africa, Uganda, Zimbabwe (Until Mugabe ruined it) Botswana, Malawi.

There is Singapore, Malaysia, Brunei, I think Burma was largely as it is now?

Iraq and Iran are largely British creations, Oman, Kuwait, Saudi Arabia, Yemen, Israel, Palestine.

Quite a few really.

New Zealand is much as it was, the treaty of Waitangi saw to that.

And Egypt was always Egypt although its current borders are probably British?

South America apart it is probably simpler to name the Countries Britain hasn't had a hand in creating lol.

The entire Raj, which had no infrastructure to speak of before Britain built the canals, roads, railways, introduced crops like tea, introduced a government and civil service and welded the various princely states into a nation. Sadly, as soon as we left it fell apart and they murdered a couple of million people within a few weeks of independence. Since then various parts of the old Raj have equipped themselves with nuclear weapons and gone to war with each other on occasion. It is continuing to fragment, and will presumably collapse like the old soviet union did.

>"an already established government to the British Empire (e.g. India)"

No such thing – India was not a single nation.

Read up on Cecil John Rhodes.

how bout the us