There are many ways to join the Brotherhood of Masons.
One of the easiest ways is if you know someone who is a Mason ask them.
Freemasons will not approach you to become a Mason, you have to approach them.

If you don't know anyone personally then asking around at work or in your social group
or in the next family gathering. You will be surprised who walks up to you and shakes your hand
and will say "I will be proud to be your sponsor in to Masonry".

An e mail to a Lodge member on this site may get you started on your Masonic journey.

Don't forget that there are a lot of Lodges in the London area and they all meet on different days of the Month.
So if there is a Lodge that meets on a certain night and you know you are available on those nights
then that could be the Lodge for you.

Good luck and enjoy the "Journey".