I don't think they were meaning to say digging is cheap, just that the cost would be minor when compared to the total costs of other nuclear power projects. It cost something like $34B to add two reactors to Plant Vogtle in Georgia [1]. And cost overruns at a project in South Carolina ended up with an estimate of $25B before the company filed for bankruptcy and the project never got finished. Whereas most of the estimates I have seen are in the single digit millions per mile for drilling. But even $100M in drilling would be minor compared to $25B.
FWIW... Finland has built a deep geological nukewaste repo. Wikipedia's numbers are: 520m (1700 feet) deep for 818 M€. Source of the money: "The State Nuclear Waste Management Fund has approximately €1.4 billion from charges for generated electricity."
HS2 estimating £33 million per kilometer, in the absolute best case of a horizontal fairly shallow tunnel through earth and clay. A 1km hole straight down? I suspect that's going to start at 100m and go up unforseeably from there.
But! What's not apparent until you read the article is that the planned reactor is .. 76cm across. That is, it's designed to fit down an oil well. Effectively you get "artificial high temperature geothermal", a hot object buried deep underground that you circulate water past.
