Theresa May is under pressure to change equality law so trans people are not forced to undergo medical tests to prove their gender identity.
Jeremy Corbyn said the Prime Minister could offer the DUP - who have failed to back same-sex marriage in Northern Ireland - a free vote on the legislation to get it through Parliament.
He also called on her Government to offer a formal apology to men with historical gay sex convictions - going further than the posthumous pardon they were granted in January.
The Labour leader was speaking at a Parliamentary reception organised by Pink News to mark 50 years since the Sexual Offences Act decriminalised sex between two men.
He said: “The Government posthumously pardoned thousands of men convicted of offences that once criminalised homosexuality.
“I welcome it in a sense, but why would we seek a pardon for something that should never have been a crime in the first place?
“They deserve an apology, an apology for everything that went on.”
He added: “A love of one person for another should never be considered a crime, and I think the case of Alan Turing has been instructive for many people.
“He saved millions of lives by deciphering Nazi codes, a gay man who served this country and helped bring about the end of the World War, criminalised for his sexuality and then chemically castrated at the hands of the state. Immense physical and psychological harm which led to his suicide.
“A pardon for a man so unimaginably wronged seems insufficient to say the least. I think we should welcome an apology to every gay person who was ever persecuted.”
He said the Prime Minister must also deliver on promises she made to the LGBTI community during the election campaign and back changes to the Gender Recognition Act that would allow trans people to self-identify.
The commitment, which Labour made in its manifesto, was not included in the Conservative manifesto.
The Labour leader said his party would back the legislation and the PM could allow the DUP and her own MPs a free vote so she could make good on her pledge.
He said: “Fifty years ago, homosexuality was decriminalised.
“Today, the struggle goes on for LGBT rights for all. In particular, we must advance trans rights. Discrimination has gone on too long. The Gender Recognition Act does not allow trans people to self-identify their gender and forces them to undergo invasive medical tests. This is wrong.
“Labour recognised this in our manifesto, pledging to update the Act. Theresa May told Pink News that ‘changes need to be made’ but failed to include anything on this in the Conservative Manifesto.
“So, I say to her today, Labour will help you keep your promise. Bring forward a Bill to update the Act and improve trans rights and Labour will back you. You can give your MPs and the DUP a free vote and Labour will make it law.”
Education Secretary Justine Greening, who became the first openly gay female cabinet minister when she announced she was in a same sex relationship last year, also spoke at the event.
Greening said in her previous role as International Development Secretary she saw that many countries were on “a journey” in terms of what LGBTI rights were granted.
She added the UK Government had “more steps to take” but did not address the issue of trans self-identification directly.
She said: “What was interesting to me when we brought forward the legislation for same-sex marriage was that this debate was reignited all over again and in a way it gave us a chance to take stock of where Britain was now.
“And actually Britain is in a much better place. It is a much more tolerant, genuinely much more inclusive country than I think we have ever been.
“But we have got a long way to go. And there are too many pockets of communities in our country where LGBT rights is something that were a mistake, and they think that things have gone too far and things should go back to how they were.
“And my personal view on all of this, whether it is LGBT rights or indeed gender equality, unless you are winning this battle then you are de facto losing it.
“That’s why we have to keep pushing for progress and there are lots of steps that need to be taken, and that I am determined to see us take as a Government going forward.”