Zero-waste shopping can mean a number of things: buying articles designed to last, eg, good-quality T-shirts that last for years rather than cheap ones that lose their shape after a couple of washes; buying secondhand from charity shops, eBay, etc, or obtaining goods from Freecycle, Freegle, etc; and repairing or repurposing items.
It can also mean using your own containers when you buy unpackaged groceries. Shops like As Nature Intended offer the opportunity to refill washing-up and laundry liquid bottles, and many Lush products are unpackaged.
As for food, loose fruit and veg are readily available from shops of all kinds, but it isn’t all that easy to buy other kinds of products in loose form. The Zero Waster has a comprehensive list of places where you can do just that, as well as much other useful information about avoiding waste.
The Source Bulk Foods has just opened in Chiswick, at 24 Turnham Green Terrace. It has a range of about 450 products, including flour, rice, cereals, honey, oil and vinegar, as well as cleaning and personal care products. You can buy whatever quantity you need and fill your own containers. Have a look next time you are in the area.