Londoners are generally quite casual, even those who work in offices. There are some business districts - The City and Canary Wharf are the largest - where most wear suits but beyond those areas, jeans and casual tops are common. Even at a West End theatre you are likely to see a lot of casual clothing worn.
White sneakers often help us identify an American visitor but that doesn't mean we all wear fancy shoes as, again, the effortless style of a Londoner is relaxed and casual. Comfortable shoes for your time in London are a must as we walk a lot here. I was amazed to see an American family join a walking tour with no coats, high heels and wearing what I would describe as 'smart business wear'. They were wearing black, which is often considered the 'default' clothing color in London, and they coped with the walk but they did stand out.
Buying the souvenir "I heart London" t-shirts and sweatshirts is a great idea for wearing back home as it says to all, 'I had a great holiday!' but wearing them while in London will make you more noticeable as a visitor/tourist.
An interesting tip was to wear a t-shirt from a London sports club - maybe a Karate or Judo club - to give you extra credibility and remove any vulnerability. Football t-shirts (Americans call it soccer, we call it football) are common on match days but if you wear a football club's shirt be aware of the attention it can attract in a rival team's neighborhood. You'd be unlikely to meet any aggression but there may be a few comments.
As London weather is most definitely 'changeable' it makes sense to wear layers here. It can be hot on the tube even when it's cold outside. We often notice someone from out of town as they get hot and bothered sooner than a local.
Of course, everyone needs a bag for their daily essentials (travel pass, money, bottle of water, etc) but a large daypack worn on your front is a big no-no. While, I agree, it's safer than feeling concerned someone may touch your bag if it was on your back, it makes you stand out so brings the wrong attention. A backpack slung over one shoulder is a much more common sight in London.
I like a mini-backpack myself (just big enough for a good book and a bottle of water, plus I carry a spare shopping bag in there in case I do need to carry more later) but a shoulder bag works well too. If you wear it across your body you will look slightly more like a tourist than a local but you do need to feel safe too. Keep your bag quite small as you really don't want to be carry half of your worldly possessions around town all day.
Make sure your bag has a zip as I find it disconcerting to see a bag on the floor of the tube, by the seat of a passenger, and I can see all of the contents - including high-risk items such as a wallet and a smartphone. Always keep your bag zipped closed - what's the point of having that zip if you don't use it? - and avoid storing your mobile phone in a jeans back pocket as pickpockets like that. I'm a big fan of my Scottevest Chloe Hoodie as it has an inner breast pocket with a zip for my phone, a clip for my house keys, and loads of extra pockets for other goodies to carry including a camera and map.
Try to avoid having a camera and map in your hand as you walk around London as that just offers more pointers for undesirable attention. But don't be afraid to take photos in central London (we'll talk about this more later in the article).
Avoid using a bum bag/fanny pack as they really are the domain of tourists so, while I know they can make you feel more secure knowing all of your valuables are close, they also make you stand out for the wrong reasons.
We are not required to carry an Identification card or passport so it's best to keep your valuables in your hotel safe. Only keep one bank card in your wallet so you have access to funds from an alternative card stored safely at the hotel in case anything does happen. For example, I often take a small amount of cash and my credit card when heading into town and leave my ATM/debit card/cash card at home. I can always take it out to get more cash later but no point risking losing both.
See the full list of good advice: How Not To Look Like A Tourist In London.
More Good Advice: Things To Not Do In London.