Yup, as others have indicated, the age for qualifying for a bus pass (for both men and women) was originally set at 60 because that was (at the time) the age at which a woman would qualify for her State Pension.
When the State Pension age started to rise, the qualifying age for a bus pass began rising with it. That means that, based upon the original way of calculating it, the qualifying age should now be 67 (for someone who's just approaching 60). However the administrations in Wales, Scotland and Northern Ireland decided to abandon the link between the State Pension age and the bus pass qualification age and stick to 60. So it's only in England that the qualifying age for a bus pass is 67 (and will rise to 68 when the State Pension age does). Elsewhere in the UK it's still 60.
London is just the same as the rest of England in that the qualifying age for a bus pass (which can be used across England) is 67. However it's known as a Freedom Pass because it also provides free travel on London Underground and National Rail services within the capital. Separate to that though, Londoners can get a free Oyster Card (which is only valid in London, not in the rest of England) at the age of 60. [The Mayor of London is hoping to keep that scheme in place but, due to the rules imposed by the Government in return for state assistance to keep TfL afloat, it's continued viability is currently in doubt].