Here are three reasons:
Without the ECHR all sexual acts between men in Northern Ireland and Scotland may have remained illegal
Although male homosexual acts were partially decriminalised in England and Wales in 1967, they remained criminalised in Scotland until 1980 and Northern Ireland until 1982. The reason why Scotland and Northern Ireland decriminalised male homosexual acts was as a direct result of the judgment in Dudgeon v the United Kingdom by the European Court of Human Rights. The decriminalization in Scotland anticipated the adverse judgment against the UK, and the decriminalization in Northern Ireland was required by the judgment. Without the intervention of the Court this legislative change would have been significantly slower or not happened at all.
Without the ECHR there would be inequalities in the 'age of consent' for homosexual and heterosexual sex
The minimum age for homosexual and and heterosexual acts remained unequal in the jurisdictions of the UK until the decision in Sutherland v the United Kingdom deemed this to constitute discrimination. In England and Wales, Peers in the House of Lords were so resistant to lowering the age of consent for (what was then) acts of buggery and gross indecency that the Labour government was required to use the Parliament Acts 1911 and 1949 to force legislative change in 2000. Without the Convention it is highly unlikely the UK Parliament would have taken this course of action.
Without the ECHR gay men and lesbians might not be able to serve in the armed forces
Until judgments by the Court, most notably Smith and Grady v the United Kingdom, gay men and lesbians could not officially serve in the UK armed forces. When the Court held that the armed forces policy of discharging gay men and lesbians interfered with their Convention rights, the UK government was required to ensure changes were made to end this practice. The widespread cultural change, which has resulted in the contribution of gay men and lesbians to the armed forces being recognized and celebrated, was given an important 'kick start' by the Court.