Phillip Berry, 62, said he and his husband Michael Davis, 77, received two weeks’ worth of post at once in their home on Grafton Gardens on Saturday, February 14.
This included letters for a hospital appointment which had already happened for Michael, who is on the waiting list for a colonoscopy.
It comes as Royal Mail confirmed deliveries in the SO16 area have been affected by sickness absence.
Phillip said if they hadn’t downloaded the NHS app, they would never have known about this appointment.
He added that they never had the chance to fill out a pre-appointment medical questionnaire, which they were supposed to receive by post.
Michael’s original surgery was cancelled due to the fire at Southampton General Hospital, and the couple are stressed that they may miss any news of the appointment being rescheduled because of unreliable post.
Phillip said: “We’re concerned that they’re going to contact us about Michael’s surgery being rescheduled and we won’t know.
“It’s still important to have the paper versions of these letters, you can’t always find the information you need for an appointment online.”
He added: “It’s just really appalling if you need the post to know about these things.”
Phillip also said they are still waiting on a credit card statement from NatWest, which is almost three weeks late now, and he has noticed other neighbours have not been receiving post either.
He said: “How can we rely on it?
“When you’re going through a stressful time you need to be able to rely on the post.”
The couple are also under added stress because Michael’s mother has recently been given weeks to live.
Phillip said: “It just adds to the worry, when we know we’ll need the post to communicate with solicitors, receive a death certificate and other things.
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“We shouldn’t be expected to go online for everything when we have already elected to get it by post.”
Royal Mail said high-volume senders, such as banks or NHS trusts, are increasingly using Royal Mail’s economy product, which is delivered five days after posting, rather than First or Second Class.
The spokesperson added: “We understand how frustrating it is when post does not arrive as expected, and we want to reassure people that the vast majority of mail is being delivered as planned.
“Resourcing challenges have impacted deliveries to Grafton Gardens over the last week but the office is clear of post as of today.”