The USA used to have "Service Merchandise" [1], which was a similar concept -- it was a "catalog showroom", you'd walk the isles, find the product you wanted and write down the code and then after you check out, you'd wait for your product to appear on a conveyer belt from the warehouse. They went out of business in the early 2000's.

I don't know of any similar stores that are still in business.

[1] https://en.wikipedia.org/wiki/Service_Merchandise

SM was the third in that category (locally), after Consumers Distributing and Best Products. There was also one named something like DAK (not the Drew Kaplan electronics-specific thing); they had a store at Camden and Union in Campbell/San Jose.

Years earlier, there was Unity, but they had few stores and were mostly catalog.

One could argue that Sears was the original catalog+store model.

I still remember seeing my SNES come down that conveyor belt.

Ikea still works this way with larger items.

Ikea

Ikea's a bit different, in that you collect the items yourself in a warehouse, and it's mostly furniture-centric. Argos is more like a small Amazon in a building; they sell all sorts of stuff.

I'm not aware of any current US equivalents, though now-defunct chain Service Merchandise was similar, and Sears was a US pioneer of catalog ordering and did have some overlap in catalog usage in their retail stores, back when they still did catalogs.

You can also order online at Argos and pick up although the one time I tried that it worked out slower than ordering in-store. Argos has never done so well as they could do, in my opinion. Not sure Sainsbury's are going to be the ideal solution to this either?

Many major chains have free ship-to-store ordering. I don't take advantage of it much but, especially if you have logistics issues with getting large or expensive packages delivered, it's not a bad option.

"Catalog showrooms" used to be more common in the US. Service Merchandise is the name that pops to mind. Lots of places have something like this as part of a hybrid model. B&H Photo is one example that I frequent.