Abd el-Fattah, a software developer and blogger who rose to prominence as an activist in the 2011 Arab Spring, was jailed for five years in Egypt over a social media post, a sentence that followed several previous spells in prison, including before and after the uprising.
Greste on Monday joined Abd el-Fattah's mother, who has been on a hunger strike ever since Egyptian authorities failed to free her son on a scheduled release date of September 29 last year.
The duo demonstrated with placards and pictures of Abd el-Fattah just outside the entrance to Downing Street as they sought a meeting with UK Prime Minister Keir Starmer.
Both Starmer and United Kingom Foreign Secretary David Lammy have raised Abd el-Fattah's case with their Egyptian counterparts a number of times, with Lammy doing so most recently on Thursday, the UK's Foreign Office said.
"We continue to press on his case at the highest levels of the Egyptian government," a spokesperson said.
"Officials from the Foreign Office continue to call for consular access to Mr El-Fattah and for his release."
Greste, who plans to stage a 21-day hunger strike, was in a neighbouring prison cell to Abd el-Fattah in 2013.
Greste had been accused of helping a terrorist group while on assignment for broadcaster al-Jazeera, charges he said were bogus and politically motivated.
"He saved my life. He was an inspiration to me. I want to now repay what he gave me," Greste told Reuters at the demonstration, crediting Abd el-Fattah with guiding him through a "really dark" period in prison.
Egypt's interior ministry did not immediately respond to a request for comment.
Laila Soueif, Abd el-Fattah's mother, who says she has lost nearly 25 kilograms in the hunger strike in which she only consumes water and hydration salts, said she had met UK officials including National Security Adviser Jonathan Powell to press her son's case.
"I've now become completely fed up," said Soueif, 68, a mathematics professor.
"I almost wish I would collapse and this thing would get resolved one way or another."
