One of Britain's top spies has described the Islamist Muslim Brotherhood as "at heart a terrorist organisation" and labelled Hamas and Hizbollah as surrogates of the Iranian state.

In a rare - and extraordinarily candid - public appearance, Sir Richard Dearlove, who was head of MI6 at the time of the 9/11 attacks, told an audience at foreign affairs think tank Chatham House to be wary of the Brotherhood's influence in Egypt.

Speaking at a conference on Wednesday marking the 60th anniversary of British-Israeli diplomatic relations, Sir Richard said: "I, for one, have absolutely no illusions about what the Muslim Brotherhood is, or can be. It can be a social organisation. It can be a political organisation. But it is at heart, in my view, a terrorist organisation."

He said it was not clear in what direction events in Egypt might lead. "What is the medium to long-term threat from the Muslim Brotherhood in Egypt? I worry greatly about what may or may not happen in a semi-democratic Egypt which is trying to change its constitution very fast, at speed faster than it is possible to create new political organisations." He added that the Muslim Brotherhood was by far the most organised political movement in Egypt.

The former head of MI6 made clear that co-operation between the UK and Israel on Iran was "immensely important". He added: "Of course it does overflow into the role of Hamas and Hizbollah, both of which are largely, in terms of the way they behave towards Israel, Iranian surrogates."

He was also worried about Islamist influence in Libya, adding that the rebel stronghold of Benghazi was "rather fundamentalist in character".

Sir Richard was also frank about British-Israeli relations. He said there were common security interests against a background of significant policy differences. "The relationship with Israel is difficult. But that doesn't mean it's not important and that it's not given close attention professionally and politically".

Expanding on the distinction between "professionals" (intelligence officers) and politicians, he added: "On a day-to-day level there are a lot of hot potatoes being dropped in the direction of ministers, so that the professionals can ensure they have political cover for whatever they are doing."

He revealed that there remained a significant level of suspicion from British spies towards their Israeli counterparts. "There is no doubt that Israel plays by a different set of rules than the rules that we observe in the UK. I'm not going to expand on that, but I will just have to leave it to the imagination."

He also noted that UK politicians and MI6 were not always certain they could share intelligence with the Israelis. "I was quite frequently in discussion with Robin Cook as Foreign Secretary about what should or shouldn't be passed to our Israeli colleagues - and there are obvious reasons for that, because we could never guarantee how the intelligence might or would be used by the state of Israel."

Speaking on the same panel, Uzi Arad, former chairman of the Israeli National Security Council, used the occasion to criticise the UK's anti-terror strategy and its concern with addressing the grievances of the Muslim community.

"This gives me an uneasy feeling," he said, especially when it was linked with the Middle East peace process.

Israeli President Shimon Peres used the conference to pledge his support for the "revolutionaries" of the Arab Spring. "It is a great moment and I pray for their success," he said. "The Arab world is entering the 21st century. I feel they can win. What can we [Israel] contribute to help?...To use the short time of the open window to bring an end to the conflict with the Palestinians. We have to take away this excuse that they [the Arab rulers] fight for the Palestinian people."

Foreign Secretary William Hague, who gave the closing keynote speech at Chatham House, restated the government's support for Israel and its right to defend itself. However, he added: "This does not mean that we will agree on every expression of that right or on every one of Israel's actions."

He restated the UK government's feelings of increasing frustration with the stalled peace process and urged Israel to reconsider over settlement building. "Time is working against the interests of all those who want peace. The British government has made clear our concern about ongoing settlement expansion. We believe it is illegal, an obstacle to peace and a threat to a two-state solution."

More provocatively, he called on Israel to learn lessons from the uprisings across the Middle East. "One of the most important lessons from the Arab Spring is that legitimate aspirations cannot be ignored and must be addressed. It cannot be in anyone's interests if the new order of the region is determined at a time of minimum hope in the peace process."

In a separate intervention at the conference, outgoing Israeli ambassador Ron Prosor delivered a stinging attack on British universities for tolerating extremism on campus, becoming the focus of the boycott movement against Israel and even educating members of the autocratic elites of the Middle East

The ambassador, who is due to become Israel's envoy to the United Nations, said there had "never been so much hostility, hatred and hypocrisy towards the state of Israel in British universities."

He taunted UK higher education institutions for their connection to Middle East dictatorships. He joked acidly that he blamed the British for the unrest in the Middle East as they had been responsible for educating Saif al Islam, the son of Libyan dictator Muammar al-Gaddafi and Bashar al-Assad of Syria.

He added that although government relations were good between the two countries, he was worried that relations between the two societies were less positive.