The Prime Minister “raised concerns” about the welfare of Nazanin Zaghari-Ratcliffe during a phone call with Iran’s President Hassan Rouhani, Downing Street said last night.
Mum of one, Nazanin is due on trial on as yet unspecified charges.
The 37-year-old was arrested while she was at an airport with her daughter Gabriella after visiting her family on holiday.
Iranian officials have previously accused Mrs Zaghari-Ratcliffe of leading a "foreign-linked hostile network"
Her British husband Richard Ratcliffe, 41, has dismissed the accusation. His petition on Change.org currently has more than 794,000 signatures.
He said: "All my family were very pleased to hear that the Prime Minister had raised Nazanin and Gabriella's case.
"We are thankful to her for her personal care and hope the Iranian authorities will answer it positively. I hope that they are home together soon".
A Downing Street spokeswoman said: "The Prime Minister raised concerns about a number of consular cases involving dual nationals, including that of Mrs Zaghari-Ratcliffe, and stressed the importance of resolving these cases as we worked to strengthen our diplomatic relationship."
Ms Zaghari-Ratcliffe, who is a project manager with the Thomson Reuters Foundation, travelled to Iran on an Iranian passport.
She is being prosecuted in Tehran's Revolutionary Court and her case is to be handled by judge Abolghassem Salavati.
Her two-year-old daughter had her British passport taken away and is staying in Iran with her grandparents but is unable to leave the country.
For more information about this petition go to change.org/freenazanin or email firstname.lastname@example.org