It would be a long tunnel/pair with only the 2 portals but I thought it was really the stations in London which cost a fortune.
Realistically it isn’t a great comparison to compare the Elizabeth Line, which is under at most 40m of London Clay, to your proposal for a tunnel nearly 1km under hills, the engineering challenges are vastly different between the two.
That being said as a very of the cuff rough statement, yes it would probably cost less than the Elizabeth Line.
However the cost is very dependant, at its very core on alignment and length, which will dictate emergency access requirements; and how many tunnels your going to have to dig through the entire mountain, and if you have to create emergency stations. Where the tunnel goes, and therefore the distances and depths these have to be dug can have big effects.
You also have to factor that such a tunnel hasn’t been dug in the UK before, so importing machinery and skill from abroad will be expensive, however the cost may be more comparable to projects abroad because there are fewer of the factors which tend to increase the cost of UK infrastructure projects around planning for an underground tunnel. There’s no way to come up with even a rough estimate without fairly detailed investigation.
Just give the engineers the remit and it could be done. They dug Standedge tunnel by hand, after all.
It’s certainly not impossible, or hugely difficult, but remind me how many people died digging that tunnel by hand?
Engineers of the past achieved quite a few things quicker and cheaper than we can now, but that was usually at the cost of human life.