David Cameron yesterday dismissed a call for a conscience clause to be added to British law which would allow greater protection for those holding religious beliefs.

His comments came during the weekly Prime Minister's Questions in Parliament, as a response to a question from Democratic Unionist MP Gregory Campbell.

Campbell suggested that legal action taken against a Christian-run bakery in Northern Ireland, which refused to decorate a cake with slogans in support of gay marriage, signifies "an oppressive threat to religious freedom," and asked for the PM's thoughts on the issue.

"I was not aware of the specific case, and I will of course go away and have a look at it," Cameron replied.

"However, I think that a commitment to equality – whether we are talking about racial equality, equality between those of different sexes, equality in terms of people who have disabilities, or, indeed, tolerance of and equality for people with different sexualities – is a very important part of being British."

His comments will no doubt disappoint those hoping for safeguards to be put in place for religious conscience.

The UK's most senior female judge, Baroness Hale, recently suggested that that a "more nuanced approach" may be necessary when dealing with issues of religious liberty in court, and highlighted the possible addition of a conscience clause in order to "make reasonable accommodation for the manifestation of religious beliefs".

"If the law is going to protect freedom of religion and belief it has to accept that all religions and beliefs and none are equal. It cannot realistically inquire into the validity or importance of those beliefs, or any particular manifestation of them, as long as they are genuinely held," she added.

Cameron's apparent dismissal of this idea is therefore an interesting addition to the debate, especially given his declaration that Britain is a "Christian country" just last April.

Himself a believer and, he says, an active member of the Church of England, the PM also insisted that "what we need more of is evangelism" – his latest comments, however, do not seem to fit well with this stance.

"It is disappointing that the Prime Minister would not comment on the need for religious freedom to be protected through the introduction of a conscience clause," Campbell said following the PMQs yesterday, adding that "There have been a number of cases across the United Kingdom where so-called equality legislation has impeded the ability of people to uphold their religious beliefs".

Campbell insisted that "Tolerance needs to be a two-way street" and branded the Irish bakery case "totally unacceptable".

Colin Hart, of the Christian Institute which is supporting the McArthurs – who run the Belfast-based bakery – has also denounced the Equality Commission's legal action, claiming that "It establishes a dangerous precedent about the power of the state over an individual or business to force them to go against their deeply held beliefs".

"[It] is a sign of things to come exactly as we predicted," he added.

This controversy is currently being mirrored in the US, as President Barack Obama faces increased pressures over the widely-publicised Hobby Lobby case.

The Supreme Court last week ruled in favour of the family-run arts-and-crafts chain, which wanted exemption from a clause of the Obamacare legislation which requires employers to provide the morning after and week after pills as part of their health insurance plans.

Christian owners the Green family argued "These abortion-causing drugs go against our faith...We simply cannot abandon our religious beliefs to comply with this mandate" and were granted the right to uphold religious objection in a landmark ruling on 30 June.

This has caused significant outrage, however, as liberal groups argue that the Court's decision signifies a failure of women's rights. Some organisations have now consequentially withdrawn their support from Obama's plan to prohibit discriminatory hiring practices amidst fears that he will grant religious groups exemption.

The Guardian reports that Obama's executive order, which would require "government contracts to adhere to non-discriminatory hiring practices when it comes to people's sexual orientation or gender identity" has lost the support of the American Civil Liberties Union, the Human Rights Campaign and the National Centre for Lesbian Rights, among other lobby groups after Obama was petitioned by conservative religous leaders to include "explicit religious freedom protections".

However, an open letter from a second group of more liberal religious leaders was also sent to the President, urging him not to include a clause that would allow religious employers to discriminate.

"If selective exemptions to the executive order were permitted, the people who would suffer most would be the people who always suffer most when discrimination is allowed: the individuals and communities that are already marginalized," the letter read.

"Increasing the obstacles faced by those at the margins is precisely the opposite of what public service can and should do, and is precisely the opposite of the values we stand for as people of faith.

"In keeping with the principle that our government must adhere to the highest standards of ethics and fairness in its own operations, we believe that public dollars should not be used to sanction discrimination."