Apart from British Corner Shop? I’m just trying to see if there are any alternatives with low cost shipping. Any recommendations?

TIA

Relatives who want to come and visit and stay with you.

What foods in particular?

Amazon, some Walmart’s have a Brit section.

Edit: Irish shops

Normally yes, but thanks to Covid I haven’t been able to visit home nor my folks have come here. And I’m missing my British Fix🤤

A search shows some suggestions here, although they may be past their sell-buy date:
UK Foods in the US Share your finds!

Amazon works for me

What they said! I've never bought from British Corner Shop, and Amazon appears to be the same price or cheaper.

To JG - I don't think I have ever seen a Walmart with a British/ Irish section, though I am not doubting they exist, just not in my part of NC, but most if not all (IME) Kroger-owned groceries, of which I think there a more than a couple of dozen differently branded chains, cost to coast across the US, in addition to those branded "Kroger", have an international section with a selection of British preserves, teas, packets and biscuits, etc. .... But much more expensive than buying from Amazon.

FWIW. I buy very few imported groceries - I've just ordered Marmite for the first time since 2014 (in fairness my last purchase was 2x500g), and will be ordering a case of 24 cans of Heinz beans today, which I last ordered in 2017.

Amazon has almost everything you want and as previously stated usually at the best price. World Market does online and in store, they have about 250 stores all across 38 states and have most of the basics that we all like at a decent price. Most supermarkets across the country will sell Tetley tea bags, PG tips and the like and a lot will sell curry sauce. A lot of the Safeways in Colorado and Florida (and even Hawaii) have some British items.

Probably Albertson's too then, as they own Safeway.

In New York (the city area), it was super easy to get all things British. Stop n Shop had a large selection of British and Irish products in their International Aisle. We also had several small stores that catered to the Irish and could get all the shelf products you wanted, crisps and candies, as well. Next door to one of those shops was the Butcher's Fancy where they sold steak and kidney pie, bangers, rashers of 'proper' bacon, etc. Have not found anything similar here in MS.

I buy occasionally online from Parker's, sometimes I buy biscuits at the publix international aisle. Aside from that and for better or for worse I've assumed an american diet...

I usually have visitors bring stuff but, as you said, Covid-19 has meant no visitors this year so I caved and bought from British Corner Shop. The 2 things I buy are Kelloggs's Fruit and Fibre and Ariel laundry soap. Amazon are charging $18.93 for a 750g box of cereal, no prime free shipping available and arrives a month out. BCS charges $9.51 for a 500g box (shipping is £20 for up to 30kg) with immediate shipping. I've had issues with BCS, boxes sitting in Erdinger KY for almost 3 weeks sometimes, so I stopped using them but damned if I can find a better cheaper option except for friends and family bringing stuff over.

My local Publix has a British section.

Cost Plus has some good British stuff including Quality Street and other candies. I also buy Heinz beans and soup from our Kroger store (Fred Meyer here in Seattle).