Left this as a comment, but I'm dead serious: take away their chairs.
Stand-up meetings are stand-up because it makes it uncomfortable for everyone to stay too long. If people are sitting that's not fair to those standing and it's encouraging them to hang around. This is especially a problem if the meeting leader is doing it. He's setting the example, and he needs to get it short.
If at all possible have the chairs removed from your meeting room before the meetings or move them out of the way, away from the table and don't let people sit. If possible, just remove the chairs from a meeting room for a week and watch the meeting time fall.
If you can't physically remove the chairs for practical reasons, get the meeting leader to be very clear that it's a standing meeting in literal terms, make people stand up.
After people are used to standing you can stop removing the chairs, but you need to do something to drop the time, and making them stand proves you're serious about this, and it really does provide incentive to keep it short.
As Andrew notes, make sure you respect accessibility and disability concerns; if some of your team needs a chair because they can't reasonably stand up for a meeting's length, of course you should provide them a chair.
Consider sending out an email stating that next weeks meetings will be standing meetings but if anyone needs to sit they should reply back so you can accommodate them.