Hello! I would err on the casual side tbh, definitely steer clear of any of your dresses that you've described as 'wedding-y'... I've been before and it was a HOT day (if that makes any difference) and honestly the vibe was very casual - OK, a bit more glammed up/more effort made than just pottering to your local park or pub, but still very casual.
Perhaps think of the kind of thing you'd wear to a nice birthday bbq, that kind of thing?
Most men are in shorts (smart style but still shorts) and when I went most of the women were in strappy sundresses, linen trousers with cami top, floaty skirts, that kind of thing. Wedges at most (possibly not flip flops which tbf if you're going with a client you almost certainly wouldn't be thinking of anyway) or smart flat sandals/fresh clean trainers/ballet pump if you're keen to stay conservative?
If I were going tbhis week (warm weather but not baking) I'd wear a cotton/linen shirt-dress (my go-to summer frock) and flat Grecian-style sandals, a nice bag to look like I've made an effort, a straw hat and sunglasses.
I think a jumpsuit sounds perfect tbh (though I don't wear them myself, I'm too long in the body) and the only caveat would be the client you're going with, how formal/stuffy are they. And the other question, do jumpsuits actually work with flats or do they need a heel?
Boden/White Stuff type sundress sounds good too, just put a bit of thought into shoes/bag/hat/sunnies and it'll be fab.
Oh, Warehouse has lovely dresses in general and most probably in sale at the mo, I got a couple of my favourite shirt-dresses from there recently. Bet you'd only have to spend £30ish in sale.
Have an amazing time and don't worry too much about what you're wearing!!