Royal Mail has suspended deliveries to Europe, while DHL is no longer allowing some parcels into the UK.
It comes amid new transport restrictions and chaos at ports due to fears about a new strain of coronavirus in England.
Letters and postcards are unaffected, a DHL spokesman said. A shortage of storage space means some senders will have their parcels and packages returned to sender.
France has closed its borders to UK freight, creating gridlock at Dover, with emergency meetings on the 48-hour ban set to take place today.
"Regrettably, we are forced to completely halt deliveries of packages and letters containing goods to Britain and Ireland from now until further notice," DHL said, admitting it's inundated with delivery requests.
"Unfortunately, due to a lack of storage capacity, we have to return consignments with goods content and bulky goods to the senders," it added.
DHL said air freight and parcels within the UK would still be delivered.
Royal Mail has suspended mail services to mainland Europe according to a statement on its website. Deliveries to Ireland are unaffected it said.
"This is a fast-moving situation and we are monitoring things on an hourly basis. We are working to keep as many international mail services running as possible given the current restrictions around air, road, ferry and train movements from the UK," a statement said.
Items that are already in the system will be processed as normal and made ready for dispatch. These items will be held securely until we are able to get them to their relevant destinations.
"We're additionally experiencing delays to Canada and Turkey as air capacity is severely limited."
Josh Hardie, director-general of the CBI employers' group, said "no stone should be left unturned" to find a solution to the problem.
"Severe disruption at ports is the last thing Covid-struck and Brexit-weary businesses need.
"Supermarkets are well-stocked for Christmas. But across manufacturing, it's essential that disruption is as short lived as possible," he said.
