The companies in the middle of the supply chain can reclaim any VAT they paid on goods/services used in the business [1], so effectively they don't pay it.

VAT is definitely not a tax on profit, that's usually called "corporate tax" [2] which is a completely different thing.

[1] https://www.gov.uk/reclaim-vat

[2] https://en.wikipedia.org/wiki/Corporate_tax