You couldn’t be more wrong if you tried, to the extent I would question if you have even bothered to follow the link.
The author of Pedestrian Observations co-authored a comparison website for infrastructure,
Transitcosts, which compares the costs in all countries they can find records for. HSR data analysis is
here and table 5 (average cost per mile by country) show highly democratic and federalised Switzerland as well as Spain Norway, Belgian and France are the cheapest places to build HSR outside Morocco. It is easy to see that UK is a gross outlier in cost terms, and if that was addressed the country could afford a fantastic HSR network.
The website, especially its data visualisation tools, are worth a play, both for HSR and urban railway construction costs, and in neither does the UK cover itself in glory.