Yes all hotels seem to be fully booked but loads of accommodation available on AirBnb. We are staying for 5 nights so will probably go down that route anyway.
God forbid if the scousers or Rags get there it would be intolerable. If you've not been to Kiev, there's not that many watering holes so they'd be impossible to avoid.
My advise if the worst happens, head out on a cheap internal flight to Lviv. A great City.