Apple TV 5.2 can't find wireless keyboard

Hi,

I have a 2011 iMac with wireless keyboard, magic mouse and magic trackpad and I just bought Apple TV yesterday. I have repeatedly tried to pair my keyboard with my Apple TV using bluetooth but Apple TV never finds my keyboard, the screen just has the spinning circle with the words "searching". I have brought my keyboard into close proximity to the Apple TV, just in case it was too far away, with no change.

My keyboard, trackpad and mouse are all discoverable on my iMac and still nothing.

The batteries are not old, the keyboard is set to "discoverable" and my iMac connects with Apple TV with no issues, so I cannot for the life of me figure out what is preventing my Apple TV from recognising that there is a compatable bluetooth device available.

Any help would be greatly appreciated as it's an absolute PITA to use the remote to enter passwords etc.

TIA

Emma