Traveling troupes were the more common form of theatrical entertainment in England before the construction of permanent theaters. The most commonly known form of this was the Italian Commedia dell'arte troupes.

Now the dates you're talking about would technically fall under the category of Medieval theatre. It's a little unfair that this genre covers as wide a range of dates as it does (~400-1400 BCE), but we can blame the Renaissance scholars for that.

Theatre was still in a public forum, but it usually consisted of a town square or a church. A lot of the theatre was liturgical, as one could expect from the Medieval period. There were morality plays, which was an allegorical hero's journey; mystery plays, which were plays directly taken from various Bible stories; and masques, which were essentially highly costumes dumb shows which singing.

These types of performances were happening all over Europe, so London would definitely have taken part in them.