Drayton Manor. Probably top-tier rather than second tier. Got 3 or 4 decent rollercoasters and whatevs. Not been for about 10 years, it now has a Thomas [the Tank Engine] Land.
On a similar effort to Beamish Museum, the Black Country Living Museum is just up the road in Dudley. Again, not been for about 10 years but it’s alright. Mines, boiled sweets, fish and chips, canals, etc