Sweden alone produced 1,9 million tons of sugar beets 1937, so there's some potential. I am sure Finland produced quite a bit too.
That's worth between 200,000 and 400,000 tonnes of actual sugar - 10-20% of prewar imports. If Sweden had a surplus I'm sure the UK would be happy to buy it, but you're looking at no more than 1 ship a month to deal with it - not a big impact really.
UK might also have increased deliveries from the French colonial Empire since it won't be going to occupied France
What occupied France? The Germans currently occupy about six square feet in Alsace, and even at their peak it was a pretty small fraction of French territory - probably less than in WW1.
Very true but I think it had more to do with the logistical capability in terms of vessel availability and other higher priorities for purchasing and shipping goods. TTL with no U-boat war and Malaysia and Burma still in British hands, these demand restrictions are likely butterflied away. As will be the Bengal famine. Rationing of some goods will exist TTL as per the excellent analysis above. But won't be nearly as severe as OTL.
Italy not being in the war has a huge impact, as does France - that means the UK can stick much more closely to prewar trade routes, and use existing supply chains.
Notice the importance of the routes through Suez and to the River Plate - both of these remain open ITTL since the U-boat threat is vastly lower, and the British probably don't even run convoys past Freetown or Gibraltar. IOTL the vast majority of that shipping was transferred to the Atlantic convoys and the produce sourced from the US, simply because the losses were too great and too much shipping was needed on the other (much longer) routes. Here, because convoys aren't needed as much and the U-boat threat is vastly lower they aren't forced to do so.
Objectively, an increase in Irish holdings of these wouldn't have been a major additional problem but maybe the UK government felt otherwise.
What did the Irish government think?
I wonder if the products Ireland had a surplus in (milk, butter, bacon and perhaps beef) were simply not as critical in the UK's eyes? Or the UK didn't want to pay for them with goods the Free State wanted? Still seems odd to me.
I take his concerns with a pinch of salt myself but he wasn't totally irrational so I do at least imagine that there would be some capacity for additional egg, butter and bacon supplies. They weren't on ration down South (as a generation of Ulster smugglers could testify!)
Bacon the shortage was 210,000 tonnes, eggs the shortage was 18 million great hundreds of eggs (2.2 billion eggs). Again, Ireland can supply a bit more, which would certainly be appreciated - but the UK's population and hence demand for food was rather large compared to most of the countries being suggested. Holland and Denmark were the major suppliers before the war, but that was largely because they were pioneering what we now know as factory farming - nobody else really had the technology yet.
