A gay couple from Barnsley are threatening legal action against the government after discovering they will not be able to marry on 29 March, when the Marriage (Same Sex Couples) Act comes into force, because they are already in a civil partnership.

Michael and Paul Atwal-Brice entered into a civil partnership in 2008 as marriage was not an option available to same-sex couples at the time.

They planned to become one of the first couples to convert to marriage when the legislation came into force and had chosen their suits and ordered a wedding cake when they were hit with what Paul calls a "legal bombshell".

When they went to book a registrar for their wedding, they were told they could not marry unless they first formally dissolved their civil partnership – in effect getting a divorce.

The government has not yet decided how same-sex couples can convert their civil partnership to marriage. The process will not be finalised before the end of 2014, a spokeswoman for the Department for Culture, Media and Sport (DCMS) admitted.

It was an "unfortunate anomaly", said a spokesman from the gay rights group Stonewall, who said the organisation had been lobbying hard on the issue.

Paul, 34, who has twin seven-year-old sons with his partner Michael, 29, said: "We're being penalised because we're already in a civil partnership. No couple should be asked to divorce or dissolve to be able to get married. To dissolve a civil partnership, you have to go to court, and you have to have a valid reason. Wanting to get married is hardly a valid reason to dissolve a civil partnership, so we would effectively have had to commit perjury."

Dissolution of a civil partnership is only possible on grounds of unreasonable behaviour, two years' desertion, two year's separation (with the respondent's consent), or five years' separation (without consent).

"For us this is about equality," said Paul. "But it's not just the principle of the situation – there are legal and practical difficulties if we were forced to divorce. If our civil partnership were dissolved there would be a period of time when we would not be each other's next of kin, for example."

The men want to raise awareness of the problem, believing that many other couples may unknowingly be in the same situation.

Now the couple have instructed lawyers after being told that because of delays in implementing parts of the act, they would have to get a formal dissolution before they can marry.

Their solicitors Irwin Mitchell have written to the culture secretary, Maria Miller, warning of potential judicial review action if the issue is not resolved satisfactorily.

Irwin Mitchell believes there are breaches of British equality and human rights law, and that the government has failed to take into account all relevant considerations when creating the equal marriage laws.

Zoe Round, a specialist family lawyer at Irwin Mitchell solicitors in Sheffield, said: "Our clients are naturally devastated at the prospect of having to go through a formal dissolution before they can get married. They had been waiting for this legislation to be agreed for years and now, at the final hurdle, are finding that the process just doesn't seem to have been thought through.

"All necessary considerations should have been taken into account by the government before the announcement was made that the first same-sex marriages could happen from 29 March 2014.

"We have written to the government to ask them to implement the process of conversion from a civil partnership to a same-sex marriage as was intended by parliament in section 9 of the act, so that couples that want to marry don't have to go through a dissolution of their civil partnership before their ceremony.

"Why should they be forced to get a dissolution just to remarry? It seems absurd and we are supporting them in their fight to remedy the situation. If the issue cannot be resolved then we may have no choice but to seek a judicial review in the high court."

A DCMS spokeswoman said: "We are continuing to work hard to ensure that couples wanting to convert their civil partnerships into marriages are able to do so as soon as possible. We aim to do this before the end of 2014.

"It will take a little longer because we need to introduce completely new procedures and processes. This contrasts with the work to make new marriages for same-sex couples possible, where we have been able to build on existing processes so implementation is more straightforward.

"The conversion process will ensure that couples in civil partnerships do not have a break in their legal relationship, which could have implications for matters such as their pension entitlements."