King Abdullah died aged 90. He was buried in an unmarked grave in Riyadh after Friday prayers.
Today, David Cameron and Prince Charles will join other world leaders in Saudi Arabia to pay their respects and meet the new king, Salman.
Archbishop of Canterbury The Most Revd Justin Welby told Sky News: "Freedom of religion is essential and freedom to express Christian faith in Saudi Arabia is something that should happen.
"A few weeks ago there was a group of migrant workers arrested for holding a private service in a flat. That's not right.
"But I know that King Abdullah himself - it's a complicated place Saudi Arabia, like all countries - King Abdullah himself is someone who has worked very very hard on these issues and has contributed much and I think it's right that the prime minister should send condolences and should recognise what he's done over the years."
However, campaigners say the decision to lower flag in England and Wales makes a mockery of the country's human rights record. There has been recent outrage focused on the public beheading of a woman and a sentence of 1,000 lashes meted out to the creator of an online blog.
The head of Amnesty International Salil Shetty said: "The Saudi regime seems insensitive to human rights and human dignity and unfortunately they are also protected by many Western countries because they have oil and because they are seen as allies in the fight against terrorism."
The UK government's Department for Culture, Media and Sport (DCMS) reportedly sent out the request.
It's believed officials said it was a matter of protocol and that the formal request had been made by Buckingham Palace, which is also flying its flag at half mast.
In a wide-ranging interview, Archbishop Justin also called religious leaders to hold responsible those who engage in extremism or abuse in the name of their religions.
"I've never been involved in any abuse; I wasn't ordained when a lot of the things happened. But in my job, I'm accountable. I have to stand up and talk about it."
He also said he was looking forward to the consecration of the first female Bishop in the Church of England, which is taking place early next month.
