Those were the most influential voices but they've kind of all fed off and reinforced each other. I'm less familiar with the UK, so I can only speak to the US, but Reagan heavily pushed the debunked trickle down economics theory to justify cutting taxes on the rich, a core part of his economic policy (and all Republicans since then). Many who consider themselves Libertarian have since picked up and championed those same policies, but really just about everyone under the greater conservative umbrella embraces them because they justify their true economic goals which are to funnel as much money into the hands of the wealthy as possible.

From an economics standpoint the core lies of Republicans boil down to a) cutting taxes, especially on the rich, always improves the economy and makes everyone richer, and b) the private sector is always better in every way at providing goods and services than the government is.

They then use those two lies to justify removing government services (usually couched as eliminating wasteful spending) and giving the rich tax breaks and loopholes. They'll often claim to be providing tax cuts to everyone, which is true-ish in the most technical sense, but when you look at the way it actually plays out the rich end up getting massive cuts, while the poor see little if any actual tax cuts. Meanwhile they severely hurt the poor and middle class by removing government services they rely on and either not replacing them with anything, or replacing them with private sector services that are inferior and/or more expensive.