Conglomeration of what we have so far
To everybody who contributed on this thread, thank you kindly. For anybody reading I have compiled most people's suggestions/fixes below so people can easily track what we've already tried, in addition to possibly trying a few themselves to hopefully resolve the problem on wireless connection with 8.1.
If there are any additional suggestions I'll happily edit this post to incorporate them.
Thank you again for your continued patience in helping us diagnose the problems.
Router Settings:
1) First and foremost, try restarting your router. Turn it off, unplug and leave for 30 seconds, then plug the power back in and see if your wireless performance is more stable.
2) Change the wireless encryption on your router. By default, most routers are set to WPA Auto or WPA Auto/WPA2. Change the setting to WPA2 only.
3) If the wireless operating channel is set to ‘automatic’, change it to stay on a static channel instead. This may increase performance.
4) If you use a dual-band router, try connect only to the 2.4GHz network, or only to the 5GHz network. Is there any difference?
5) If your router supports dual-band but can only use one radio band at a time, try it change from 5GHz to 2.4GHz (or vice-versa) and see if it makes a difference.
iPhone Settings:
1) Ensure the iPhone is updated to the latest version of iOS 8. To check this, go to Settings > General > Software Update.
2) Hard reset. To do this, hold down the power button and the home button at the same time until your phone restarts.
3) Reset Network Settings. To do this, go to Settings > General > Reset > Reset Network Settings. This will restart your iPhone and take a few minutes to complete. Please be aware that this will wipe any saved networks.
4) Turn off wifi networking. To do this, go to Settings > Privacy > Location > System Settings, and toggle the wifi networking option to off.
5) Enable Airplane Mode, leave for 30 seconds, then turn Airplane Mode off. This normally helps for about an hour.
6) Disable Bluetooth.