Mirroring and Airplay won't work on 2013 iMac and Macbook Air

I’m having problems with Airplay and Mirroring on an iMac (late 2012) and Macbook Air (2013), both of which should support the functionality. Neither computer can see Apple TV even using Air Parrot. An iPhone 5S on the same network can see Apple TV and Airplay works flawlessly.

To clarify further, under System Preferences / Displays / Airplay Display the iMac and Macbook air both display “No devices detected”. Home sharing and Airplay via iTunes also don’t work.

The network setup is the following:

ADSL Gateway Netgear DGND3700 providing connectivity, DHCP and NAT.

Apple Time Capsule (4th Gen) providing WIFI (WAN port connected to an ethernet port of DGND3700).

Each device is connected to the same local network in the range of 192.168.9.x using DHCP and all Macs are using OSX Mavericks.

I’ve tried everything I can possibly think of including rebooting the ADSL router multiple times, rebooting and hard resetting Time Capsule, disabling any firewall but nothing seems to help.

Can anybody suggest a solution I may try?

Many thanks,

Max