More than five years have passed since Rebecca Steinfeld and Charles Keidan tried to form a civil partnership at their local register office, only to be told they could not because they were not of the same sex.

On Tuesday after spearheading a long campaign to change the law, they returned to Chelsea Town Hall and walked out as civil partners, joining thousands of others who made history by formally entering into the newly recognised unions on the eve of a new decade.

Flanked by friends and family and joined by their two young daughters, the couple said their wish to form a civil partnership had been “rooted in our desire to formalise our relationship in a more modern way, focused on equality and mutual respect.”

Following Steinfeld and Keidan’s victory at the supreme court in 2018, it is expected that as many as 84,000 ceremonies will be conducted in 2020 as couples take advantage of a right originally legislated for LGBTQI couples.

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The first is believed to have taken place in Carmarthenshire, where a register office opened at two minutes past midnight on New Year’s Eve for Jake Rayson and Emma Wilson.

In London, Steinfeld heralded the new dawn by telling the assembled media and wellwishers: “There is now a space for new, more modern possibilities for people to express their love and commitment to one another.

“The urgent need to reform cohabitation law so that social policy keeps up with the reality of family life in modern Britain has been brought into greater focus. And by ending the unrivalled position of marriage we have helped to create the space for deeper discussions about giving legal recognition to other types of personal and caring relationships, such as those between friends, siblings and co-parents.”

Quick guide Explainer: civil partnerships Show Hide Civil partnerships were created in 2004 as a means of allowing same-sex couples to enter into a union that guarantees them similar legal rights to those who are married. They were limited to same-sex couples but in October 2018, following a supreme court ruling declaring the existing position discriminatory, the government announced that heterosexual couples would also be entitled to enter the arrangement. There are differences between the two forms of union, partially symbolic and partially matters of substance. For a marriage, the ceremony is solemnised by the couple saying a prescribed form of words; in a civil partnership, the couple can simply sign a document. Marriages can be conducted through either a civil or religious ceremony, at a registry office, church or wherever a venue is licensed. Civil partnerships are secular events, although partners can choose to hold a religious ceremony on the day. Civil partners cannot declare, for legal purposes, that they are married. Civil partnership certificates include the names of both parents of the parties whereas marriage certificates in England and Wales include only the names of a couple's fathers – for the time being. In terms of annulment the rules are virtually identical, although the clause that permits a marriage to be dissolved if one partner is 'suffering from a venereal disease in a communicable form' does not apply to civil partnerships. Likewise, adultery can be grounds for a married couple to divorce though it cannot be relied upon to end a civil partnership.

Those in civil partnerships and those who are married enjoy the same tax breaks and benefits – such as the marriage allowance and bereavement payments. Surviving civil partners are treated the same as widows or widowers in terms of rights to state pension.

While those who are married and in civil partnerships enjoy extensive legal rights, those who are merely cohabiting – 3.3 million couples at the last estimate – have no legal protections or property rights if one of them dies.

The couple were joined for the registration by their two children, Eden, four, and Ariel, two, and their parents and friends who acted as witnesses.

Afterwards, they described what had happened inside the register officer as a “very stripped back,” simple process, for which they had paid the statutory minimum fee of £46.

There was no ceremony as such, they added, but they had taken the opportunity to say a few words to each other in front of their children that had been “skipped out on” in the course of five years of campaigning.

Later, they adjourned for a simple family lunch at a nearby pub, before planning to host a New Year’s Eve party at which friends were invited “to bring the food that they love to cook or makes them feel loved up.”

The journey had not come without a significant personal cost, as Keiden spoke candidly about the toll on his mental health.

“Against all odds, we succeeded in a legal battle against the government and then, they did what we asked for all along. Not many people can say that.” he said.

“But we both know with everything gained, some things risk being lost, or at least unspoken. Through this long journey and hard-fought battle, our mental health has suffered, our ability to be civil to each other has been tested, and, crucially, we missed out on that important moment to state clearly what we mean to each other – not just what we’ve become in the eyes of others,” he said.

Elaborating on that later in an interview, he told of how he had started to feel very tired earlier this year “in ways I couldn’t explain” after their historic court win.

“I think that I just burn out both physically and mentally. I spoke to the doctor and employers and took five weeks off work to really just take time to recover from the thing we have been through. I am glad I was able to do it and I think the conversation about mental health has changed in society in the last few years and have allowed me to accept that we are not as formidable as we think.”

Those involved in the couple’s campaign said they were aware of as many as 80 other civil partnership ceremonies happening around the country on Tuesday, and there were believed to be many more.

The academics, who live in Hammersmith, west London, suffered defeat at the court of appeal but were given the go-ahead for a supreme court hearing in August 2017.

The panel of supreme court justices, including the court’s president, Lady Hale, heard the couple’s case in May 2018, and the judges later held that the Civil Partnership Act 2004 was incompatible with human rights laws on discrimination and family life.

The minister for women and equalities, Liz Truss, said: “Congratulations to all the couples who are having their civil partnerships today. I am proud that we have helped give thousands across the country the option to have a civil partnership and celebrate their union in a way that works for them.”