I totally disagree. I think you can expect formality to a much greater degree than the previous poster states. I am not certain that I would wear a Summer dress at all, nothing you would wear to a friendly lunch, go more fomal than that: a fitted linen dress, not flowery or floaty, and with jacket. And yes, take stockings and wear them. The UK is generally speaking a lot more formal that the US. When I first arrived here from London, the total lack of formality at seemingly any occasion at all dismayed me.
Skirts, yes, but again, go fitted and not flowery or floaty. And yes, wear stockings. If you err on the side of formal and then they are not, you have not screwed up. If you err on the side of informality and they are formal, you could screw up unbelievably. Many British people entertain negative stereotypes about US citizens, loud clothes, loud voices and opinions: don't give them any fuel. That's my advice, as a Londoner. And you said it yourself, "the office is professional." If so, it will remain so, despite changes in seasons, and despite being located on Canary Wharf.
Cheers, and good luck!
Clare