The claim comes amid continuing diplomatic fallout after a British arrest warrant was issued last week against Tzipi Livni, who served as Foreign Minister during Israel's Gaza offensive last winter. The warrant was withdrawn when it became clear that Ms Livni, now leader of the opposition, was not in the country. Its existence apparently prompted her to cancel a trip to attend a meeting in London.
President Peres described the incident as "one of the greatest political mistakes" that Britain could have made and calling for the law to be changed. "Everything is based on ... a hostile majority public opinion," he said last week. "The British promised they would fix this and it is time that they do so."
Gordon Brown and David Miliband, the Foreign Secretary, have each expressed their concern and their opposition to the warrant.
The campaign by Hamas takes advantage of an aspect of law in England and Wales that allows anyone to apply for an arrest warrant for alleged war crimes without the need for a prosecuting lawyer. The identity of the person or organisation that applied for Ms Livni's warrant has not been made public, but Hamas says that it initiated the move.
The Foreign and Commonwealth Office said yesterday that the Government was "looking urgently at ways in which the UK system might be changed in order to avoid this sort of situation arising again".
Diya al-Din Madhoun, who heads the Hamas committee set up to coordinate the campaign, said that it had "all the political and military leaders of the occupation in our sights", although he did not specify its future targets. He told The Times: "This has absolutely become our policy."
The committee of legal specialists was established after the Gaza offensive to investigate allegations of war crimes carried out by Israeli forces. It compiled 1,500 cases over several months and started to encourage alleged victims to file charges against Israeli leaders in countries such as Britain, Spain, Belgium and Norway, according to Mr Madhoun. The committee intended to put the victims of alleged crimes in touch with lawyers and legal institutions in Europe, he said. "We do this as a government trying to protect our people and prevent these massacres from recurring."
Hamas had not been involved directly in filing legal cases or contracting lawyers, he said, but its governing administration had acted as a facilitator. "We have provided a group of independent lawyers in Britain with documents, information and evidence concerning war crimes committed by Israeli political and military leaders, including Ms Livni."
About 1,400 Palestinians died in the conflict. Many were civilians, although Israel and the Palestinians have disputed exactly how many. Mr Madhoun said that the countries such as Britain were chosen because their legal system allowed for the prosecution of foreign citizens for crimes not committed on their soil. He criticised demands for Britain to change its laws.
The Israeli daily newspaper Ma'ariv said that lawyers acting for the committee "go into action each time an Israeli senior official arrives in a European country in which they are operating. The 'incrimination file' formed by Hamas on the respective senior official is then dispatched to them, and from there it is sent to the court with a request for an arrest warrant."
Other organisations have tried to use European legal systems for a similar purpose. In 2003 a Belgian court ruled that Ariel Sharon, the former Israeli Prime Minister, could be tried in Belgium for war crimes over his role in the notorious Sabra and Shatila massacres of 1982.
In July this year the National Court of Spain issued arrest warrants against six Israelis including Binyamin Ben-Eliezer, a former Defence Minister, over war crimes allegations dating back to 2002. Several other Israeli politicians and officials are believed to have avoided travelling to Britain because of the threat. In September a British court declined a similar legal action filed against Ehud Barak, who is still serving as Defence Minister and has diplomatic immunity.
"These reports show that it is not human rights that drive these suits but an anti-Israeli campaign at the service of Hamas," Yigal Palmor, the Israeli Foreign Ministry spokesman, said.
In Gaza Mr Madhoun urged European countries to resist Israeli pressure.