The figures here:
House of Lords - The Economics of High Speed 2 - Economic Affairs Committee
although dating back to 2012 and 2013 show that there is little overcrowding on trains on the West Coast line (paras 146 to 154) or elsewhere. Paras 146 to 188 make interesting reading both as regards overcrowding and fare policies.
On the Scarborough-Manchester-Liverpool line, passengers standing is common, especially at rush hours as it is a commuter line as well as an "intercity" line.
In the report linked to above, mention is made of longer trains and this seems a solution to overcrowding which isn't much considered in England and Wales. Even on York race days, the trains from Scarborough are still only 2 or 3 units.
Scotrail seems to have a different approach. Pitlochry has a population of 2,776 and is on the Perth-Inverness line. When we were here last November, the three coach platform was being extended to take nine coach trains.