Depends how far you're going and how much you can carry. Kings Cross to Inverness I would need at least three litres, a lot to carry along with other luggage, food etc.
Okay perhaps that was excessive, but I panic if I don't have a good supply of water when I'm stuck on a train. Maybe two litres then. Still too much to comfortably carry.
2l in 24 hours is the recommendation, isn't it? Anyway, buying bottled water is a mug's game. Take 1l with you in a reusable bottle, that's loads.
2l of water weighs 2kg. That is not heavy.
Heavy is relative! I understand you are quite a big strong guy. I am a short female!