It depends on the train company and where you put it. If it's over 1m in any direction, in theory you can be charged extra for it, but I'm not sure how much and I've never seen it happen.
LNER have more crew than average, so are more likely to check, but if you check the layout diagram for the train you're using (sometimes the easiest way is to try to reserve a seat), you might spot either a large luggage rack or some other open area. Don't put it in the seats except as a last resort because if you do, I suspect you'll get told to move unless it's really quiet. If it's an LNER Azuma, coaches B and L look like your best bets for a large luggage cupboard. And I'd try to avoid carrying it into the buffet coach where staff will almost always see it!