The shortest an entirely new-build line could possibly make would be about 13.5 miles, so that'd imply a non-stop run and a maximum permissible speed of 110miles/hour. So I'd say, technically achievable, yes. But realistic? Not a chance.I’m not sure how Manchester to Bradford will be able to be undertaken in 30 mins, or Bradford to Huddersfield in 12 mins, but I imagine they aren’t either.
A large amount of property and other protected land is rather in the way, so most of such a short route would be tunnelled. Topography is also near as challenging as it comes.