+1 for the idea of adjusting your profile so that it reflects your correct height, or simply leaving it blank. It's not uncommon for men and women to lie about their height and weight on dating sites, but it does not make for a good first impression when the first thing you think upon meeting is 'wow, he/she lied to me.'

I like your ideas for your date. Concert and coffee/food afterwards sounds like a nice first date, and so is having ideas in mind for later on. You could plan on doing those other things on your own, to extend the day in London, and ask her to come along if it feels right in the moment. My first date with my current boyfriend was meant to be dinner and a movie, but we had such a good time that we wound up going to a concert and then out for a late night snack as well.

I hope you have a great time!