Royal Mail has suspended deliveries to Europe, while Germany's DHL is stopping some parcels into the UK.
The moves, just days before Christmas, come amid new transport restrictions and chaos at ports due to fears about a new strain of coronavirus in the UK.
Letters and postcards are unaffected, DHL said. A shortage of storage space means some senders will have their parcels and packages returned, it said.
France has closed its borders to UK freight, creating gridlock at Dover.
"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.
"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," it said. Parcels it already has will be "held securely" until it can transport them it said.
Haulage firms have also seen growing disruption, forcing supermarkets to try to dampen fears that the chaos will cause food shortages.
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.