Question phrases to make sure that everything is understood correctly

I am looking for the best question phrases to make sure that everything is understood correctly.

– Trains to London leave on Mondays, Tuesdays, Wednesdays, Thursdays, Fridays, Saturdays and Sundays.
– Do I understand correctly that trains to London leave daily?

Does this sound nice? Would am I not mistaken that do? Any other ideas?

"Do I understand correctly that...?" is perfectly grammatical, but very formal and stilted. It will be understood, but marks you as either posh or not a native English speaker.

"Am I not mistaken that...?" implies that you think you are mistaken, so I wouldn't use that in this context.

A more colloquial way to get confirmation is to assert the conclusion you want confirmed, but using a questioning intonation pattern (or a question mark in written English):

"So trains to London leave daily?"

You could also say

So in other words, trains for London leave daily?

Let me make sure I've got this right: trains for London leave daily?

What about?

Am I right, that trains to London run daily?