OK, so I got bored, and...
View attachment 178802
Y = direct service at least 2 hourly - 1 point
ish = limited direct service - 1/2 point
N = no direct service
Settlements chosen are GB urban areas above 300,000, from
this list. Yes, I've left Birkenhead in for no particular reason. And I've split out Leeds and Bradford, and Southampton and Portsmouth, based on the well-established and completely scientific criterion of Having A Reasonably Large Football Club.
Ignoring locations that don't have a well connected intercity station nearby, or a massive city in between it and the rest of the country, I'd say that the priorities should be Leicester, Teesside, Swansea, Hull.
Reading gets the prize for punching above its weight.
Liverpool isn't actually that badly connected.