The Prime Minister David Cameron paid tribute to Saudi Arabia's King Abdullah bin Abdulaziz after the monarch passed away at the age of 90.
Abdullah's death followed a battle with a lung infection and he has been succeeded by his 79-year-old brother Salman.
"I am deeply saddened to hear of the death of the Custodian of the Two Holy Mosques, His Majesty King Abdullah bin Abd Al Aziz Al Saud," Cameron said.
"He will be remembered for his long years of service to the Kingdom, for his commitment to peace and for strengthening understanding between faiths.
"My thoughts and prayers are with the Saudi Royal Family and the people of the Kingdom at this sad time.
"I sincerely hope that the long and deep ties between our two Kingdoms will continue and that we can continue to work together to strengthen peace and prosperity in the world."
But Saudi Arabia has come under fire from human rights groups because of some of the country's actions.
Amnesty International warned that Raif Badawi, a Saudi blogger, remains at risk of receiving his remaining 950 lashes over the coming weeks for "insulting Islam".
The prisoner of conscience was sentenced to 10 years in prison and 1,000 lashes, followed by a 10-year travel ban, a ban on using media outlets, and a fine of one million Saudi Arabian riyals ($266,600, £177,450).
Badawi created the Saudi Arabian Liberals website, which the Saudi court ordered to be closed.
Elsewhere, Human Rights Watch called on police to release two women who tried to drive car across from the United Arab Emirates to Saudi Arabia.
Lujain al-Hathloul, 25, and Maysa al-'Amoudi, 33, were detained for flouting the country's ban on women drivers.
"After years of false promises to end its absurd restrictions on women, Saudi authorities are still arresting them just for getting behind the wheel," said Sarah Leah Whitson, Middle East and North Africa director for HRW.
"The Saudi government's degrading restrictions on women are what bring shame to the country, not the brave activists standing up for their rights."