LONDON, Sept 15 (Adrian Croft/Reuters) - A British law limiting citizens' rights to seek the arrest of foreign politicians for alleged war crimes took effect on Thursday, removing a thorn in British-Israeli relations.

The law amends legislation which Israel had protested about, saying it exposed its high-profile officials to the threat of arrest for alleged offenses if they visited Britain.

Under the old law, private individuals could start criminal prosecutions, including for international war crimes, by applying to a magistrate for an arrest warrant.

Israel demanded Britain change the law in late 2009 after reports that former Foreign Minister Tzipi Livni would have risked arrest on war crimes charges over the 2008/09 Gaza offensive, had she not canceled a visit to London.

Last year, Israel said it had stopped sending delegations to Britain for routine strategic talks out of fear pro-Palestinian activists would seek their arrest for alleged war crimes.

The new law requires the consent of the Director of Public Prosecutions before an arrest warrant can be issued in universal jurisdiction cases, where a case involves alleged crimes committed outside Britain.

These new changes to existing law will ensure the balance is struck between ensuring those who are accused of such heinous crimes do not escape justice and that universal jurisdiction cases are only proceeded with on the basis of solid evidence that is likely to lead to a successful prosecution, Justice Secretary Ken Clarke said in a statement.

Activists attempted to obtain warrants under the old law to arrest visiting foreign dignitaries such as former U.S. Secretary of State Henry Kissinger, senior Chinese Communist Party official Bo Xilai and Livni, who is now Israeli opposition leader.

Israel's Foreign Ministry has said that the legal jeopardy faced by Israeli politicians and military officers could damage Britain's efforts to play a role in Middle East peacemaking.

Human rights group Amnesty International condemned the change last year, accusing the government of handing war criminals a free ticket to escape the law.

In Israel, Livni's Kadima party said Britain's ambassador to Israel, Matthew Gould, had informed her of the change to the law.

A Kadima statement said Livni welcomed the decision, telling Gould: I am happy that the arrest warrant against me opened the eyes of the British and will bring an end to the cynical use of the British legislation against commanders and soldiers in the IDF (Israel Defense Force). (Additional reporting by Ari Rabinovitch in Jerusalem; Editing by David Stamp)