LONDON, Oct 6 (Reuters) - Israeli opposition leader Tzipi Livni was in Britain for talks with British Foreign Secretary William Hague on Thursday, the first senior Israeli figure to visit since a change in a war crimes law kept her away for fear of arrest.

Livni and Hague would meet to discuss bilateral relations and events in the Middle East, British officials said.

She arrived weeks after Britain approved changes to a war crimes law that had led some Israeli politicians and officials to stay away from the country and clouded relations between the two countries.

Her centrist Kadima party said she was visiting at Hague's invitation.

The Palestine Solidarity Campaign called for a protest near Prime Minister David Cameron's Downing Street residence on Thursday to protest at Livni's visit, saying the British government must arrest war criminals, not invite them to London.

Kadima said an arrest warrant had been issued in Britain in 2009 against Livni, foreign minister during the three-week war Israel launched in the Palestinian-ruled Gaza Strip in December 2008.

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

The new law requires the consent of the Director of Public Prosecutions before an arrest warrant can be issued in cases involving alleged crimes committed outside Britain.

Israel urged Britain to change the law in 2009 after reports Livni would have risked arrest on war crimes charges stemming from the Gaza offensive had she not canceled a visit to London.

Since then, the Palestinians have shifted their focus to a bid for statehood at the United Nations, where Palestinian President Mahmoud Abbas formally lodged an application for full membership last month.

As foreign minister, Livni led peace talks on behalf of Israel. Those negotiations came to a halt after the Gaza offensive in late 2008.

I cannot say for sure that we can end this the next day, it is not around the corner, Livni told the BBC when asked about prospects for a settlement with the Palestinians.

But it is clear to me that we need to explore more and we build trust and this is something which is missing today, said Livni.

She said she believed that two states for two peoples represent the Israeli interest.

(Reporting by Adrian Croft; Editing by Angus MacSwan)