She was arrested with her infant daughter Gabriella on April 3 2016 at Tehran’s Imam Khomeini Airport as she prepared to board a plane back to the UK after visiting relatives.
Mrs Zaghari-Ratcliffe, 40, is serving a five-year sentence in Tehran’s notorious Evin Prison after she was convicted of membership of an illegal group.
The trial by a Revolutionary Court in Tehran was widely condemned as unfair and she strenuously denies the charges against her.
Speaking outside the embassy, Richard Ratcliffe told the Press Association: “We’ve come to deliver her a Mother’s Day card, because obviously we can’t do that in person, and to deliver 155 bunches of flowers, one for each week she has been held.
“Flowers, partly because it’s a Mother’s Day tradition, also because that’s what people are given when they’ve been released from prison [in Iran].”
Foreign Secretary Jeremy Hunt granted Mrs Zaghari-Ratcliffe diplomatic protection earlier this month, and her husband said they are grateful.
“It’s clear that Jeremy Hunt has taken a personal commitment to Natalie’s case and he’s made some clear statements,” he said.
“Before he granted her diplomatic protection he went to Tehran. He’s done a lot to make it clear that he cares and this is a priority.
“He’s not done everything that we’ve wanted, but he’s also been clear that he’s not going to. As a family we’re appreciative of all he’s done.”
Speaking about his four-year-old daughter, who is currently living in Iran, Mr Ratcliffe said: “I spoke to Gabriella yesterday and there’s a prison visit today. We’re going to draw a card together for Granny, my mum.
“For her, it was Iranian New Year last week, so that was the big occasion that she wanted her mummy back for. That not happening, amongst a number of times that it hasn’t happened, has meant that she hopes for things but I don’t think she takes her parents’ promises entirely seriously these days.”
When asked about the stress the process has caused him and his wife, he said: “Sometimes you speak to her and she seems fine, and sometimes she’s really bleak and dark and threatening all sorts of things - but yesterday she was fine.
“Often she decides that she needs to take matters into her own hands, she had that hunger strike to get medical treatment which hasn’t been provided.
“She does threaten every so often that ‘I’ll do it again’ and it’ll be an escalation from last time. I do live a bit in fear of what will happen.
“If you don’t sort it, there will be consequences. Hopefully that’s an empty threat and it doesn’t happen but sometimes she’s in a dark place.
“[The whole experience] has brought us closer together because we’ve had to survive it. I’m hugely proud of the fact that she’s kept going, she’s kept her dignity.”
Among those laying flowers outside the embassy were his parents John and Barbara Ratcliffe.
Mrs Ratcliffe, 68, said: “We’re feeling sad, but cross. Why should this have happened to them? What’s our family done to anybody?
“That poor little girl. She’s now got a different mummy and she’ll have another different mummy when she comes out.
“The support from everybody is helping us through, it is really terrific. We just spoke to one lady who said: ‘I can see my (her) child any day. Naz can’t see her mum.’”
When asked what they wanted to see happen soon, Mrs Ratcliffe said: “Apart from the obvious, in the short term we want to see that Naz gets a bit of comfort, to get on and do whatever she’s able to do craft-wise.”
She added: “We last heard from Naz about four weeks ago, and she sounded alright but we’d been told by Richard and by her brother that she wasn’t alright. She just put on a good show for us, which was lovely.”
When asked if they felt Mr Hunt was taking the case more seriously than his predecessor, Boris Johnson, Mrs Ratcliffe said: “I’m sure now it’s taken much more seriously.
“Certainly by him [Jeremy Hunt] and we always felt (former foreign office minister) Alistair Burt really cared.
“He’s helped us emotionally a lot, and Naz’s family. But whether he can actually get her out, I don’t know. Please God that she can get out.”