With that journey you will be on Virgin trains, on one of the Pendolino's I guess.
I did a trip with Virgin trains, three hours to York, with 2 toddlers. You should get a family railcard, then phone to book seats and ask them to reserve you somewhere quiet and near to the wide-access wheelchair area.
We were on hellishly crowded trains - I couldn't even find the wheelchair area, and I basically had to leave buggy and bags in the vestibule (the size of a phone box), go and put children in seats, leave them screaming, come back to fetch bags and fold buggy.
There was no luggage space with room for a buggy, all small boxy spaces aimed at briefcases I think. I had to take all three wheels off the Phil & Ted's much to the amusement of fellow passengers.
To be fair, the nearby passengers helped to calm the boys down and were really kind about the travelling circus that we turned out to be.
I did find taking this seat with me to be a godsend, you can loop the strap around the train seat and once strapped in the child is much less likely to fiddle, climb, run off, bug people etc. It's my secret weapon for travelling now and I'm hoping they will let me use it on a plane in a couple of weeks.