How can I get Apple Remote working with the BT Home Hub?
May seem like a silly question, but did you changed SSID names when you switched to the new router? If so, make sure you connect both iDevices to the new network's name and reconfigure the Remote app.

Hope this helps!
Thomas

Edit: Are you able to connect to a website from your devices on the new network? And do you still have the old router broadcasting? I ask because maybe your devices are still connected to the old network, but your PC is on the new one. If you haven't already, try going to Settings >> Wi-Fi, and verifying that the network you're connected to is the same that your PC is on. If so, and it's still not working, reset your network settings and see if that helps