Southampton is probably a city with nice typical English houses, lots of brick, pretty gardens. I could see that from the distance.
But when you are docked in port an on foot, walking distance does not take you there. I was happy to see a typical red telephone box :).
Other than that, my shopping recommendations are those of shops that are not available where I live:
Marks & Spencer, 23 Harbour Parade, Southampton SO15 1QB (in the West Quay Shopping Center)
GAP (although that is not a local business), 55-57 Quest Quay Shopping Centre, SO14 7EG (fasctinated by those British post codes – the shop are next to each other!)
I had great memories of M&S, but do not quite recall what it was, that I bought there decades ago, when in England ;)…
Then, not for locals, but for a shop that has its HQ in my country, there is a Lidl. I actually went in not to buy food basics, but to see if I´d find anything British there. I did not. But some great fresh cherries for breakfast
Lidl, High Street without a number
And I got a bit crazy in the wonderful food store of M&S, where I did not buy food (luckily I had more than I can eat, where I presently stayed at), but only took photos of all the beautiful company packages. I only bought a cool bag as it came with this presently hip slogan, „Keep cool and…“.
Absolutely every item looks stylish in a Marks & Spencer package! I couldn´t have decided anyway, or bought the entire shop… it all looked like in a Delikatessen store, lovely. I could have taken 100 or 200 photos, but I did not have the time ;).