One thing that I found a little frustrating is how specialized so many shops here are. I’m used to being able to get a lot of things in one place; in the UK things can be a little harder to track down. So, to help you out…
Groceries: This is pretty straightforward. ASDA, Tesco, Sainsbury’s, Waitrose, and Co Op are all grocery stores in the London area. Some will have the appendage “Local” or “Express” to their names; that means they are smaller. Those smaller shops still usually have an impressive selection of produce, which is good. They also will likely be open long hours seven days a week — 6 AM – 10 PM or 7 AM – 11 PM.
These stores often also have a giant counterpoint — a “Metro” or “Superstore” version. This is important because shops in the UK with a large square footage are limited to being open for six hours on Sundays, and must be closed on Easter and Christmas. So, if you arrive on a Sunday, be sure to get your shopping in mid-day if your only option is one of these larger shops.
Toiletries: Many grocery stores (even the small locals) will have a selection of basic toiletries, which can help in a pinch. But for the bigger things — and in some cases for pharmacies — you’ll want Boots or Superdrug. They have cosmetics, dental care items, hair care items, skin care items, and some limited nutrition (vitamin) options.
Health: Boots and Superdrug may have a pharmacy in them, but the NHS also has pharmacies. Look for the green cross sticking out the side of the shop over the door, and that’s where you’ll go to get cold medicine, pain reliever, etc. Like the US, pseudoephedrine is a behind-the-counter medication, but while you don’t have to sign a register, they will ask you a LOT of questions about use. They also don’t have Vicks, but I’ve found that Night Nurse is a good equivalent.
Home Goods: I’m talking about things like sheets, or dishes, or kitchen supplies. Many of the “Super” versions of grocery stores like Sainsbury’s or ASDA have home goods sections. Dunelm is a smaller-scale Bed-Bath-and-Beyond-type store that will have a wider selection of pillows / duvets. Argos is also a kind of fascinating shop that is good for somewhat cheap home goods. We were able to get a large litter box, trash cans (rubbish bins), clothes hangers, etc., from this place. What’s fascinating to me is that this is essentially a catalog shop. You look either online or in a catalog, then place your order and their staff pull it from their shelves. They also deliver, which can be nice.
Pet Supplies: Pets at Home is a good shop option. They have supplies for dogs and cats, as well as smaller animals. We were able to find a couple of things we used in the US there, but be prepared that some of the higher-end brands aren’t available in the UK. I’m sure there are equivalents, so you’ll need to play around with brands and see what your little buddies like.
Office Supplies: Maplin has small electronics like printers and such supplies (but they’re are online only), as does Currys / PC World. Ryman has stationery.