Rishi Sunak has said ministers cannot "wave a magic wand" to stop Christmas shortages as he warned "global" supply chain challenges will not "disappear overnight".
The Chancellor said the Government will do all it can to "mitigate" , but he accepted disruption lies ahead and did not rule out the festive season being hit.
It came as around 200 military personnel - half of them drivers - were deployed to the roads for the first time to help deliver petrol to forecourts.
Around 22% of filling stations in London and the South East still do not have fuel, according to executive director of the Petrol Retailers Association Gordon Balmer.
And despite ministers insisting the situation at the pumps, which has seen queues and panic buying, is easing, Operation Escalin launched on Monday.
Members of the armed forces arrived at the Buncefield oil depot in Hemel Hempstead to help deliver fuel to filling stations, with soldiers, in uniform and wearing face masks, spotted walking near the gates to the Hertfordshire Oil Storage Terminal.
A number of industries are seeing labour shortages, including in meat processing.
And it has prompted warnings that Christmas favourites such as pigs in blankets may not be available for shoppers this year.
Mr Sunak told BBC Radio 4's Today programme: "We're seeing supply disruption, not just here but in lots of different places, and there are things we can try and mitigate, and we are.
"But we can't wave a magic wand. There's nothing I can do about the decision by a country in Asia to shut down a port because of a coronavirus outbreak.
"But be assured we are doing everything that is in our control to try and mitigate some of these challenges."
He added: "It's reasonable that people expect us to do what we can.
"But we can't wave a magic wand and make global supply chain challenges disappear overnight.
"With regards to butchers, my understanding is that those are indeed on the shortage occupation list that we already have."
Pig farmers protested outside the Conservative Party conference on Monday as industry leaders called for a Covid recovery visa to allow firms to recruit from outside the UK.
National Farmers' Union president Minette Batters said: "They are protesting outside and they are angry, distraught and extremely upset.
"They have been calling for this, we have been calling for an emergency scheme, a Covid recovery scheme, to be put in place to avoid this very scenario."
Meanwhile, Nick Allen, chief executive of the British Meat Processors Association, said he was "surprised" that Prime Minister Boris Johnson appeared to be unaware of problems facing pig farmers when questioned on the BBC's The Andrew Marr Show on Sunday.
Mr Allen told Sky News that Christmas turkeys are likely to be from the Continent this year due to labour shortages in Britain following Brexit, and added that some foods, such as pigs in blankets, may not be available.
"We're not saying that there's not going to be food on the table at Christmas, but we're struggling to put the party food together - the pigs in blankets, the netting of gammons," he said.
"But I suspect that food can be imported and probably the turkeys might not be British turkeys but they may end up being French, or even turkeys from further afield.
"We're not saying there's going to be desperate shortages, but there certainly won't be the choices available for British food, that's for certain."
However, the chairman of supermarket Morrisons said concerns have been "slightly overblown".
Andy Higginson told BBC Radio 4's Today programme: "There are logistical issues at the moment and those are well publicised and slightly overblown.
"Supply chains in the UK are incredibly efficient and I am sure we will be able to deliver a great Christmas for customers as we go through."
The Prime Minister has repeatedly refused to rule out shortages in the wider economy in the run-up to Christmas.
As well as an estimated shortfall of 100,000 HGV drivers, businesses from meat producers to retailers have warned of empty shelves if the shortages are not addressed.
Mr Johnson acknowledged the country is going through a "period of adjustment" following Brexit, which has cut off the supply of labour from the EU.
But he insisted he is not prepared to resolve the situation by pulling "the big lever marked uncontrolled immigration" to let in more foreign workers.
He said firms should ensure their employees are "decently paid" if they want to get more staff.
The Prime Minister also spoke about the supply chain issues as he visited a Network Rail site in Manchester with Mr Sunak on Monday morning.
"That's really a function of the world economy, particularly the UK economy, coming back to life after Covid, sucking in gas in particular - there is a massive demand for that in Asia," he said.
"There is a shortage of lorry drivers actually around the world, from Poland to the United States, and even in China they are short of lorry drivers."
