Do we actually need to get two weeks of food in?

Ummm kinda misses the point if the supply chain is disrupted, or the electricity goes off and the store can't open, or if card payments don't work and you can't take out cash.....

I think it's more because the supply may be disrupted due to storms that are expected.
I wouldn't go mad buying extra stuff but ( obviously only if you can afford it )
a few extra tins of
beans ,
tomatoes,
soup,
tuna,

meat ,
potatoes ,
carnation cream / long life milk

Instant noodles
Pita / wraps ( tend to keep longer and take up less space than a loaf)

The next size up than you'd normally buy of
Flour
Oil
Marg
butter
Lentils
Rice
Pasta
Porridge / cereal
Loo rolls
Toothpaste
Pain killers / dc over the counter meds
And make sure your 'scrip meds are ordered if possible .
All that said , if you can't afford/ don't want to I am fairly sure you'd be fine unless you habitually run your cupboards empty.

Living close to a supermarket is not enough if the supermarket runs out of food is it?

I have for over 40 years had a decent stock of food, toiletries, loo rolls, washing liquid etc.

When covid hit me and DH did not have to go to a shop for over a month which was great.

At present we probably have enough food to last a good 6 weeks, probably longer. In our freezer we have bread, milk, vegetables, fruit, home made meals such as curries, shepherds pie, chilli, soups, bean burgers etc. We also have quite a lot of pasta, rice, different types of beans, nuts etc. Tinned tomatoes, baked beans etc.

I just think it is sensible to have at least some stock of food

As a 'for instance' remember Storm Arwen. Some areas had no power for nearly 2 weeks.
2 weeks of no power and trees brought down and possibly flooding means the supermarkets will close. You cannot get through to anywhere on the roads. Money cannot change hands in the absence of banks and cash registers. Etc etc.
So it is, in such circumstances, possible that - more likely if you are rural but not inconceivable in towns - you are temporarily entirely thrown upon your own resources.

There's a Preppers board here, go read some of it if you want to get your head round this stuff. Some of the people on that board were affected by Storm Arwen and other storms. It's eye opening. And don't forget cyber wars. We are in one right now, with Russia at the very least. Wasn't it somewhere in Spain just a couple of years ago everything went down for a couple of days? What about three days, four, a week? Nothing: no traffic control, police, hospitals.
Remember the fires last year in LA? They are still repairing the damage. That was a long drama. Caused by drought. Think about it.

en.wikipedia.org/wiki/Storm_Arwen

I think there’s two stories getting conflated.

The actual Gov advice mentions a couple of days of food for emergencies.
Then there are also the stories around supply chain disruption from El Niño. But the Gov is not suggesting we get weeks of food in now to protect against supply issues later.

Isn’t it to do with supply chain disruption…. The supermarket shelves could be empty in less than a week if they can’t restock?

I'm not sure why we have to stock up on food to be honest. I'm 5 minutes from a supermarket which I kind of use as my pantry anyway so in an emergency I'd just pop down there and get stuff. Wouldn't store it all at home "just in case".

This covers some of the reasons.
https://www.bbc.com/news/articles/cp931m8n3p5o