The detained writer has spent most of the past decade behind bars in Egypt and last December was sentenced to five years in prison after being accused of spreading false news.
Ms Seif said her family is “pinning our hopes” on the Prime Minister’s efforts to help.
I really believe that if he (Rishi Sunak) makes this an urgent political priority, my brother will be on the next flight to London
Mr Sunak, who is in Egypt for the major climate summit, stressed his “deep concern” about the case in a meeting with Egyptian President Abdel Fattah El-Sisi.
“The Prime Minister said he hoped to see this resolved as soon as possible and would continue to press for progress,” Downing Street said.
Earlier, Mr Sunak had told broadcasters the case was one “not just the United Kingdom but many countries want to see resolved”.
Mr Sunak had written to Mr Abd El-Fattah’s family saying he was “totally committed” to resolving the case, which he described as “a priority for the British Government both as a human rights defender and as a British national”.
After arriving in the Red Sea resort on Monday, a statement released from Ms Seif through the Freedom For Alaa campaign said: “Prime Minister Sunak sent me a powerful letter on the weekend.
“I think he intends to do everything he can to save Alaa, we’re pinning our hopes on him.
“I really believe that if he makes this an urgent political priority, my brother will be on the next flight to London.”
Mr Abd El-Fattah, a father, has been on partial hunger strike in prison, eating only 100 daily calories for the past 200 days.
On November 1 he began a full hunger strike, and on Sunday he stopped drinking water in an escalation of his protest to coincide with the summit at which numerous world leaders are present.
His switch to a water strike made the Government realise the “urgency” of the case, Ms Seif said.
Speaking to BBC Radio 4’s World At One programme, she suggested “hecticness” in UK politics had hindered work on her brother’s case.
She said: “I strongly feel that the hecticness that was happening in the Government and the change of government was … in a sense, it was a genuine excuse but also it made, like, the civil servants and the diplomats working, and the Foreign Office, have an excuse. And so they weren’t really working hard.
“I felt all of a sudden when Alaa stopped water that we were suddenly getting these calls, phone calls, we were getting the letter from the Prime Minister. So, it feels like they realised the urgency all of a sudden. We’ve been warning them that this is coming.”
Right now we’re facing the possibility of his death in the coming days before Cop27 ends. It’s a terrifying prospect
Actor Khalid Abdalla
Friend and actor Khalid Abdalla has said the possibility Mr Abd El-Fattah could die while the Cop27 summit takes place is “a terrifying prospect”.
The Crown star likened Mr Abd El-Fattah to suffragette Emmeline Pankhurst, saying he represents the “progressive fight in Egypt”.
Abdalla, who plays Dodi Fayed in hit Netflix show, said he wanted to be on the “right side of history” in speaking up for his friend.
Mr Abdalla said the reason for his friend’s detention is “completely absurd”.
He told ITV’s Good Morning Britain: “The actual reason technically for him being in prison is for sharing a Facebook post, it’s completely absurd. A Facebook post about the torture of a fellow prisoner.”
He said the writer and his family represent the “progressive fight for democracy, and social justice and a better world”.
He said it is crucial that Mr Abd El-Fattah is freed.
He told the programme: “Right now we’re facing the possibility of his death in the coming days before Cop27 ends. It’s a terrifying prospect.”
He added: “All 120 world leaders are descending on Sharm El-Sheikh right now. If all of them can’t result in Alaa being released from prison, then what hope have we got of saving the climate?”
On his support for Mr Abd El-Fattah, the actor said: “You’ve got to be on the right side of history. If you knew that there was an Emmeline Pankhurst in prison right now and you knew that there was a chance for her to get out, what would you be doing?”
In his letter to Mr Abd El-Fattah’s family, Mr Sunak described Cop27 as “another opportunity to raise your brother’s case with the Egyptian leadership” and said Middle East minister Lord Ahmad would update the family on negotiations after the summit – which finishes on November 18.
The Foreign Office has said ministers are “deeply concerned” about the incarceration of Mr Abd El-Fattah and they are “working hard” to secure his release.