In the ancient alleyways of Stone Town and across the crowded islands of Zanzibar, a quiet revolution is taking place: the issues of sex, contraception, and HIV and Aids are being tackled head-on by an unusual grouping of religious scholars and medical professionals. Their aim is to shift deep-rooted views in their devout Islamic society that contraception is a sin.

"Although the Qur'an is 1,400 years old, it is still alive," says Zuberi Muhudin, secretary of both the Zanzibar Imams Association and the Zanzibar Interfaith Association for Development and Aids (Ziada). "The verses can be interpreted for today."

In a cool office in the heart of the former slave-trading and spice sultanate, Muhudin reads from the new book Ziada has produced to examine whether family planning can be considered Islamic.

"In chapter two, verse 233, for example, it says: 'The woman giving birth should breastfeed for two years'," he says. Muhudin argues that the contraceptive effect of breastfeeding means this verse demands a spacing of almost three years between births, signifying that the spacing of children is endorsed by the Qur'an.

Compared with the Tanzanian mainland, Zanzibar has half the rate of use of contraception – just 13% in fertile women in 2011 – and more than double the proportion of Muslims, at 95%.

While tackling these controversial issues is fundamentally about the right of women to plan their families, the probable knock-on effect of curbing Zanzibar's rapid population growth is also vital, says Felister Mayala Bwana, national programme officer for reproductive health for the UN population fund in Tanzania, which gives support to Ziada.

"Even the existing 1.2 million people are too many for Zanzibar to sustain," says Bwana, without a transformation of the economy and infrastructure that is not happening. The population is growing more than 3% a year, with each woman having more than five children on average, and the population density on the dry island is 400/km2, the same as Holland.

Increasing access to contraception is at the heart of one of the UN's millennium development goals (MDG5), improving maternal health. One of the MDG5 targets is a 60% rate of contraceptive use by 2015. "That is very, very challenging," says Bwana, but can be achieved at a price. For the 45 million people on the Tanzanian mainland, there is a plan to meet the goal, costing 133bn Tanzanian shillings (£50m). There is no such plan for Zanzibar yet, despite its much lower starting point.

However, the work done by Muhudin and his colleagues is starting to have an impact: contraceptive use has crept up from 9% to 13% in the past four years.

"Religious leaders are very influential here," says Hamid Nasser, a member of the Zanzibar Aids Commission and co-ordinator of the Zanzibar Faith-Based Organisations group, which works with Ziada. "The people follow the Qur'an, but the interpretation has to link to modern ways." Condom use, he argues, is a modern equivalent of the traditional withdrawal method. He says that while it used to be the husband's decision when to have a child, religious leaders now teach that the Qur'an says both partners decide together.

"But," says Nasser, banging the table for emphasis, "there are conditions." Modern family planning methods are only acceptable if they are prescribed by a qualified Islamic doctor, he says, and aimed at protecting the mother's health. In Zanzibar, the scholars' council that sits above the imams issued a fatwa condoning condom use under these conditions.

Furthermore, Nasser says, condoms must only be prescribed from hospitals, not be handed out for free: "Children will take them and they will go everywhere." Muhudin says that nor is the idea of "controlling" population acceptable: "Even when times are hard and life is a struggle, God is the one who gives."

To make more progress, says Muhudin, further fatwas will be needed to cover other methods of birth control. While the individual imams are agreed, the scholars' council "takes decisions for the entire population", he says, and so deliberates slowly. Ziada's work on tackling these cultural issues is vital, says Julitta Onabanjo, the UNFPA's head in Tanzania.

She says: "It is not just an issue of getting contraceptive commodities to people, you have to be sure they want to use them, and are able to use them when they want to, whether to plan children, space them out or not have children at all."

Outside, above the bleached and jumbled roofs of Stone town, the minarets are joined by spires of a Roman Catholic and Anglican churches, relics of Portuguese and British influence. "Our interfaith work has been strengthened by the arrival of HIV," says Nasser. "Everyone wanted to know how to protect themselves, and, with condoms a major method, a link to family planning was made."

Bwana agrees that the increase of HIV and Aids work with family planning is a critical shift, calling it "dual protection". She says that in the past a lot of donor support shifted to the HIV and Aids crisis, leaving family planning as a lower priority. The other key link is between family planning and deaths in childbirth, which in Tanzania runs at 454 women for every 100,000 births, one of the worst rates in the world.

"If they don't get pregnant," Bwana says, "they don't die."