I didn't see the BBC programme in which this story was shared, but I do know the ministers of this courageous, radical, prophetic congregation in London. Marriage Law in England & Wales differs from that in Scotland, the BUGB and the BUS have made different responses to the legislation, so that what is possible in London would not be possible in Glasgow. To be clear, as a minister accredited by the Baptist Union of Scotland, I accept their discipline on this, as on all matters of faith and practice.
You may or may not be comfortable with the idea of churches conducting equal marriage, or even of its existence, I simply invite you to watch this short video and enjoy the joy of others...
https://www.facebook.com/BBCMusic/videos/1959905554282228/