Last week, a US-based human rights group, HRANA, said it had received information that Craig Foreman had lost about 16kg (35lb) and Lindsay Foreman was suffering from dizziness and body tremors.
Their family now says that a letter written to them asking them to end their hunger strike had not been delivered, nor had medication and other basic supplies.
“My mum and Craig are 18 months into an ordeal they should never have known,” said Bennett.
“They are weak, they are hungry, and now Craig is being punished simply for being heard. To add two more years to an innocent man’s sentence, in secret and with no chance to defend himself, is a flagrant abuse of the most basic rights any person is owed.”
Last month, two United Nations human rights experts called on Iran to release the couple, saying that proceedings against them had been marked by grave irregularities.
“Lindsay and Craig Foreman should not be in prison,” said UN special rapporteurs Dr Alice Edwards and Mai Sato.
“They appear to have been wrongfully detained, prosecuted on highly questionable grounds, and sentenced after proceedings that failed to meet basic fair trial guarantees.”
The Foreign Office has advised against all travel to Iran since 2022, saying that people can be detained there for simply for having a British passport or connections to the UK.
It has previously said it is working to ensure the Foremans are returned safely to the UK, and stressed the couple’s health and welfare was its “priority”.
The couple’s family have welcomed the appointment on Monday of the UK’s first ever envoy to support British nationals detained abroad in complex cases where there are concerns about welfare, due process or human rights.
The role will be held by the former Conservative MP and Middle East minister Alistair Burt.
Lindsay and Craig Foreman’s family said they look forward to meeting him and hope his appointment will have a positive impact on their case.