That depends entirely on:
Route
Day of week
Time of day
Whether you reserve or not (and if so, whether you choose to sit in your designated seat)
In my experience, (usual rules apply re anecdotal evidence) if you are on peak trains, peak direction, you have a good chance of having someone opposite. Sunday after lunch southbound is almost a certainty, as is half term weekends (northbound at start, southbound at end). Scotland trains are usually well patronised, albeit not that much north of Oxenholme. More than once I’ve been standing from Preston heading southbound.
There’s some other factors - if Man U are playing at home, then the half day before the match northbound on that route is likely to be busy in first. There’s a similar effect with a couple of the other big teams, e.g. Liverpool and of course Wolverhampton
Birmingham seems to be the best route for getting space in first. I guess because there are so many seats on the route and plenty of alternatives with Chiltern and LNW.