This story was corrected at 11.41am on 1 November.
Britain has been accused of bullying the Commonwealth nations as it calls into question aid structures for countries with anti-gay laws.
A Ugandan presidential official, John Nagenda, told the BBC his country was “tired of these lectures” and that the Commonwealth nations should not be treated like “children”.
Commonwealth nations are reacting to government plans to redirect aid away from central governments with poor human rights records.
International Development Secretary Andrew Mitchell said: “Taking money away from Governments does not mean you do not support that country. You find other mechanisms for trying to help the poorest with food, education and health care as well as building up business structures”
Mr Cameron told the BBC’s Andrew Marr Show at the weekend: “Britain is now one of the premier aid givers in the world – saying that our aid, actually we want to see countries that receive our aid adhering to proper human rights, and that includes how people treat gay and lesbian people.”
He was asked whether African countries would have their aid reduced if they did not reverse anti-gay legislation.
Mr Cameron replied: “We are saying it is one of the things that will determine our aid policy.”
He added: “I think if you go back in our own country’s history, there was a time when we, you know till quite recently, discriminated in lots of ways. I think these countries are all on a journey and it’s up to us to try and help them along that journey, and that’s exactly what we do.”
Many pieces of anti-gay legislation around the Commonwealth date back to colonial times and British intervention, but are still in effect as homosexuality runs counter to countries’ cultural landscapes and prevailing religious beliefs.
The Commonwealth of Nations is a voluntary collective made up of 54 member states, the majority of which are former British colonies.
While it is a requirement of membership that the states respect human rights and the rule of law, it was a focus of October’s 2011 Commonwealth Head of Government Meeting that there is little option to censure countries who fall short.
Former Foreign Secretary Malcolm Rifkind told a press conference at the Meeting: “The Commonwealth faces a very significant problem. It’s not a problem of hostility or antagonism, it’s more of a problem of indifference.
“Its purpose is being questioned, its relevance is being questioned and part of that is because its commitment to enforce the values for which it stands is becoming ambiguous in the eyes of many member states. The Commonwealth is not a private club of the governments or the secretariat. It belongs to the people of the Commonwealth.”
Nigeria has recently been seeking to strengthen the criminalisation of homosexual behaviour. Homosexuality is already punished with up to 14 years in prison and gay marriage is not recognised in the country. The new bill would make it illegal to support gay marriage.
Nigerian gay rights campaigner Yemisi Ilesanmi said the bill “would lead to harassment of people for their actual or imputed sexual orientation. It would also stifle freedom of expression and association through the proposed ban on organisations that support lesbian and gay rights.”
He added that the plans could backfire and lead to gay people being blamed for aid cuts. “We from Ghana LGBTi community think this is not enough. Cutting down aid will not bring anything other than pain and anguish to the already polarised society or country and LGBTi people will be used as scapegoats for under development in our countries.”
Addressing the Commonwealth People’s Forum last week, William Hague said: “The UK would like to see the Commonwealth do more to promote the rights of its lesbian, gay, bisexual and transgender citizens.
“It is wrong in our view that these groups continue to suffer persecution, violence and discrimination within the Commonwealth and that many members still have laws criminalising homosexuality.
“A Commonwealth that lives up to its values is one where all its citizens are free to live their lives in a safe and just society.”