Chief Rabbi Ephraim Mirvis said Mr Peres "was the greatest living example of an unshakable belief in the pursuit of peace against all odds".
Former British PM Tony Blair also paid tribute describing the Nobel Peace prize winner as "a political giant".
Mr Peres died aged 93 on Tuesday, two weeks after suffering a stroke.
He was one of the last of a generation of Israeli politicians present at the new nation's birth in 1948, serving twice as the country's prime minister and once as president.
He also won the Nobel Peace prize in 1994 for his role negotiating peace accords with the Palestinians a year earlier.
Rabbi Mirvis said Mr Peres "gave hope to millions of people" that a peace deal would be achievable.
He added: "Tragically, thus far, we have not succeeded. But from Shimon Peres we learned that we must never let go of that audacious commitment to peace, even when all around us are ready to do so."
He went on: "For those of us whom he inspired during his remarkable lifetime, we say: No matter what the future holds, your legacy lives on in the Jewish people who will never rest until we achieve our eternal dream of peace among the peoples of the world."
Mr Blair paid tribute to Mr Peres on twitter, writing: "Shimon Peres was a political giant, a statesman who will rank as one of the foremost of this era or any era, and someone I loved deeply".
The chief rabbi of the UK and Commonwealth has paid tribute to former Israeli PM Shimon Peres, describing him as a "true giant amongst men".