Oh Jeez. I'm so sorry to hear this.
Thank goodness they have you as a parent, who will take action to protect them...I know you will sort this out one way or another.
What;s been said is correct. Look up their anti bullying policy, and quote it at them - I would actually email so you have a 'paper trail'. Face to face meetings are the favourite of HTs who want to BS you into submission. If necessary follow up any meeting with an email clarifying anything said and agreed.
Ring around a few schools, get recommendations from other parents and so on, that's a great way to check schools out.
They will tell you if they have places but you'll have to apply formally through the LEA and can download their 'in year admissions' form from the county council website (under education section).
You send this off with a few choices of schools for each child, and they process it and let you know about places in a few weeks' time.
IB is right, it could take a while to move them all over. But it will probably be worth it.
I'm trying to do the same at the moment, sadly our place disappeared between ringing the school and our application being processed, but ds2 is on the list for the school so if he is given a place ds1 will go to the top of the waiting list.
Good luck on Monday...I'll think of you, as I'm doing something similar 