He doesn't get free healthcare, he gets socialized healthcare that he pays for with taxes. It's not a gift out of magic, it's a political and economical choice.
The US and the UK do actually spend the same percentage of GDP in government taxation on healthcare. It's just that for the same amount of money Americans get treatment for the poor and the elderly, whereas the British get universal coverage. So, relative to the US, the UK coverage of the wider population is actually free. There is no greater sacrifice, or higher level of taxation to pay for the extra coverage.
References are quite easy to find, but here's one, from the Telegraph, quoting data from the OECD:
If he's not paying the tax then his parents either are or did. Same here in Australia, it's just a part of the basic standard we are prepared to be taxed for.
I love the free healthcare, which is paid for by our higher taxes, which I am very happy to pay because of the benefits I (and, more importantly, other people worse off than me) get as a result.
Higher taxes in the UK do not, however, explain why the same product is 1.6x more expensive here. Part of the different will be accounted for by VAT (20%) and import duty (14% for this product, I think), but nowhere near all.
Incidentally, the US has import duty too. (But I think it's generally lower than for the UK.)
Also simply that the UK is a smaller market with less competition, and UK consumers are largely used to being charged at these levels (I lived in the UK in the early '90s, and the "$ = £ for imported tech goods" equation was exactly the same then). Importers are going to charge as much as they can until people stop buying, and apparently, people aren't.
I think this is particularly the case for specialized niche equipment, as it tends to be bought only by those who really need/want it, so demand tends to be relatively price-inelastic...