There isn't an equivalent all-women team, but there has been at least one female member of the Reds in the past.
The Reds are selected from serving fighter pilots and they do a 2 or 3 year secondment into the team. To be picked for the team, pilots need to have a certain number of flying hours and to have flown operationally. Many are instructors. There are still not that many women in the RAF flying fast jets, so it's extremely unlikely there'd ever be 9 of them in the position to be in a display team.
Incidentally there was a (civilian) parachute display team at a flying club I belonged to. Some of the female parachutists were fed up of never being asked to join, and formed their own team. Pretty soon they were getting more bookings than the men 😁 who were absolutely furious!