Jeremy Corbyn has written to Theresa May calling for an urgent effort to establish humanitarian corridors in Aleppo and a boost to Foreign Office resources to aid efforts for a ceasefire.

The Labour leader, whose speech on human rights was interrupted on Saturday by activists including Peter Tatchell – who said he had not spoken out enough on the Syria crisis – said the government had to step up its pressure on regional actors and the UN.

Assad regime forces and Iran-backed militias, supported by Russian warplanes, now control the vast majority of the besieged Syrian city. Civilians and activists in east Aleppo tweeted final pleas for help from the international community overnight and texted journalists farewell messages, saying they faced imminent death.

On Tuesday morning, a UN spokesman cited multiple reports that 82 civilians had been killed across four different neighbourhoods. “The reports we had are of people being shot in the street trying to flee and shot in their homes,” he said.

Corbyn said he was writing to “request an urgent and concerted effort from the government to press for an end to the violence and a UN-led ceasefire” and said all parties had to take responsibility to protect and extract civilians.

“The creation of UN-brokered humanitarian corridors and the issuance of effective advance warnings of attack to the civilian population is a basic requirement,” he wrote.

“The rules of war are being broken on all sides. Labour has long condemned all attacks on civilian targets, including those by Russian and pro-Syrian government forces in Aleppo, for which there can be no excuse.”

Tatchell and activists from Syria Solidarity UK disrupted a speech by Corbyn on Saturday to demand he do more to condemn the actions of Russia in the Syrian conflict.

Tatchell, who said the Labour leadership must increase demands for aid airdrops, said: “What is happening in Aleppo is a modern-day Guernica. We haven’t heard the leader of the Labour party speak out enough to demand UK airdrops to besieged civilians who are dying in their thousands.”

A Labour spokesman said: “Jeremy has repeatedly condemned the Russian military intervention and bombing campaign in Syria and called for an independent investigation of evidence of war crimes.

“Labour has called for urgent talks to achieve a negotiated political settlement involving the main parties to the conflict, along with the regional and international intervening powers – and he has written to the prime minister today calling for a concerted effort to achieve a UN-led ceasefire and UN-brokered humanitarian corridors.”

In his letter, Corbyn called on May to “bolster and affirm the United Nations as the primary avenue for international efforts to resolve the humanitarian crisis in Syria.” Over the past week Russia, unexpectedly backed by China, vetoed a UN resolution that called for a seven-day ceasefire as Assad’s forces advanced.

“Would you set out exactly how the government will boost Foreign and Commonwealth Office resources to aid such efforts, engaging all sides, including regional powers such as Turkey, Saudi Arabia and Iran?” Corbyn wrote.

“It is time this government concentrated every effort towards working with the UN and our allies to seek a peaceful resolution of the conflict. From our perspective, the second Geneva communique should be the basis for any potential political solution.”