You should have no problems although M25 can get busy although I think it's 4 lanes on that section you'd be using, if you are not going across country. Weekends are noticably quieter.
By the way what is it about the M23 that encourages people to stay in the middle lane all the way from start to finish? It seems worse than any other motorway I've ever driven on. Shift workers heading for Gatwick half asleep?