What should I pack for London in July?

What are the best walking shoes.

Bring the shoes that you already feel comfortable in when you normally walk or exercise; you don't necessarily have to buy and break in new shoes to go to London.
Bring shorts (and maybe just one pair of pants); I find shorts are lighter to travel with than pants.
Pack for summer weather.

I have to disagree with the advice to bring mainly shorts and only one pair of trousers ("pants" in the UK are underwear, BTW). This site is loaded with information on light packing. The best overall advice is to pack clothes that you already own and like to wear. In choosing among your options, it can help to weigh each piece using a kitchen scale. A packable rain jacket is a good idea because you never know. Similarly, a light jacket or sweater. Check the forecast in the days leading up to your trip.
I agree that whatever comfortable walking shoes you already own are the best choice. If you don't currently have such a thing, I recommend visiting a local shop that caters to runners and walkers. They can advise you about what shoes are best for you. "Sneakers" or running shoes, with good support and cushioning, are generally the best option for walking around a big city like London.

I’m a huge fan of the Keen brand. Own 8 pair: slip ons, sandals and lace ups. Career was as film and TV location manager. Comfortable shoes for 16 hour days on set a must!

Keens are pricey, durable, lightweight and comfortable. They also eliminated the plantar fasciitis that existed when using sneakers.

My favorite pair are the low cut Targhee hikers. Use them here in the Land of La as well. Great for my sojourns in Griffith Park and on the trail up to the Observatory.

Also wear them to shop for groceries and over to the Sunday Hollywood Farmers Market. 10 block roundtrip sidewalk stroll.

This pair of Targhee have been to NYC, London, Havana, Belfast, San Francisco and Yosemite. Can’t tell they are over a decade old. Laces never changed. Tread stellar.

I wear Smart Wool socks with them so they don’t stink.

Peruse the Keen website
https://www.keenfootwear.com/products/womens-targhee-ii-waterproof-magnet-coral

Wearing them this Friday on my flight to Sacramento and then for 3 days in Yosemite.

As with all British weather, London in July is unpredictable. That said, July is probably the hottest month and it’s common to get several days of hot (80 def F, sometimes 90 def F) and sticky weather. After a few days this can end with a day of heavy thunderstorms after which it’s cooler and less humid. So whilst you want light clothing, a lightweight and preferably breathable waterproof jacket is worth having.

Start with the top, a hat.
Blouse/shirts, lightweight and long sleeve (sun and heat bakes the tourists meat).
Hydration, start the day prior and invest in water.
Pack your online skip the line reservations for your desired destinations. This tactic avoids standing in line with sweaty complaining tourist. Most of the major destinations offer a cafe where you can sit in cool bliss and enjoy a snack. And if you are really starting to overheat then do a bit of window shopping from the interior of stores.
Pants, go lightweight with dark colors. We rarely wear shorts.
Deodorant- ample.
Make up - less.
Shoes - we prefer slip on sketchers offering a canvas fabric and do wear lite weight socks.
Lean into the shade and strive to minimize walking in the sun.
Eat lite and consider purchasing the goods for a small picnic. So many public parks where you will find the locales enjoying the outdoors. Bring a small plastic resealable bag containing some moisturizing towels. Borrow a washcloth from your hotel.
Body odors?, time to check out the perfume samplers at local stores.
Evening offers a great time for strolling, so pick out some paths and go try and get lost.
Enjoy!

Best walking shoes are the ones that feel best on your feet walking 5+ miles a day. For that time of the year, consider a fashionable sneaker that can handle a rainy or sunny day.