Seren. First of all - well done to your DC for earning a choice of schools.
Regarding your homework question... My understanding is for Yr 7 at LU it is not especially onerous -good because it allows the kids to throw themselves into extra curricular: music, drama, tennis, photography, architecture...zumba (!) whatever - there is a pretty exhaustive range available. See the clubs list here: www.latymer-upper.org/activities-trips.html
It also gives them a chance to make friends, learn how to be organised etc. If your child has been to a prep - they will find themselves repeating a lot of Latin and French because of the large state school intake.
After Year 7, the homework ramps up. They stream from year 8 as well. Personally, I am interested in outcomes; Latymer does very well in my opinion at GCSE and A level. If they manage to achieve those results with minimal homework, then wonderful - and if the kids have to work hard at home... well, if that is what it takes. Certainly parents I know who have kids there don't think the H/W is either under or overtaxing - just about right I am told. If your child is academic he/she will still be stretched, I am assured.
Something else you should bear in mind when comparing LU and the Harrodian: LU has 7 (or 8?) classes in Year 7 , with only a couple of classes worth coming up from the Prep. Half of the new entrants are from state school. I rang Harrodian just now, out of curiosity (my DS did not apply for it, and we have accepted a place at LU). The Harrodian has 4 classes in Year 7, about 3 classes worth come up through their own prep. What does this mean? Well, your child will be entering a school where most of the kids already know each other, and even amongst the new entrants I imagine private school kids predominate. Whether this means it's a place where rich kids hang out is a subjective judgement.... Personally I would prefer my child to enter a more socially mixed school, and one in which the majority of the other children are also starting friendships afresh. But of course kids make friends quickly and there is no reason to think your DC won't quickly form strong bonds, and I'm sure the school is very careful to integrate new kids. Also lower numbers at the Harrodian will mean that your child is statistically more likely to be in the tennis team or whatever, though I'd be surprised if it were to offer the sheer breadth of activities available at a larger school.
As you mentioned Drama opportunities - When we toured LU some months back we met a very engaging Year 10 girl in the theatre area who was obsessed with stage lighting. She said she was far too shy to appear on stage, but she had found a role that fed her love for theatre. We liked that.