They also still have the NHS even though torys hate it.

Labor laws and social programs are very hard to eliminate once created because they are very popular. The US has weaker labor laws and social programs than the UK and they've been eroded since the 80s by nearly every Congress and administration. Yet we still have social security and Medicare not because Republicans love those programs, but because the remain hugely popular.

You'll note that the torys and conservatives haven't enacted or pushed for their own social programs. They've simply failed to fully eliminate what's already there.

The social programs conservatives in the US have been effective at eliminating and neutering mostly happened because of racist narratives. "Welfare queen" was very much a pejorative used to paint a picture of "urban" women living off of government assistance. That allowed for huge cuts to previous programs because they hurt the right people.