British museum is one of many London museums with free admission. It would be worth visiting it even if it wasn't free of charge.
It houses artefacts from all periods and from all over the world. Even if you think of its collection as a heap of stolen goods by the British empire, it is still worth taking a peek.
The museum holds a total of around 6,000,000 artefacts. This is a number hard to imagine, but when you spend a day or two in this institution and fruitlessly try to see everything on display you begin to understand the scale of things... there are less then one percent of artefacts on display at any given moment!
If this is not enough to convince you into visiting, there is more free stuff to make you change your mind.
There are short eyeOpener tours introducing different areas of the Museum's collection, led by volunteer guides. No booking is required. You can read more about it here.
I took advantage of this and really enjoyed seeing a couple of sections with a super nice and knowledgeable guide. I highly recommend you take advantage of this.
In addition to all that you can also take part in Hands on sessions, where you can take a close look and even touch some of the ancient artefacts. This was a first time for me to actually hold a real stone arrowhead in my hand.
Things presented were not just some copies but real stuff! How cool is that? I guess you have to be a bit of a history buff to really appreciate this, but along with great explanation from the staff this was a really great experience.
So do yourself a favour and reserve at least an afternoon within your London trip for a visit to this gem of a museum.