Wait, are you saying the Ryzen 1600 *and* a motherboard cost 200 combined? The basement price I can find is 238 quid. And that's a pretty awful motherboard, which I wouldn't recommend. 178 CPU 60 motherboard.
The Intel 8400 costs 178 quid as well, while the motherboard is 100, and I would absolutely recommend the MSI Z370-A Pro.
So, the difference is really 250 v 278. And let's not forget, if you want to OC that 1600, you will ditch the CPU cooler, so add on 25 quid for a hyper evo 212.
Anyway, I think it's much closer than your estimates suggest.
The cooler is fine. Will check prices in a minute. Maybe the 1600 has gone up in price.