Q: Networking help......

I have an Apple network, with a TC as my router.  This is wired to my BT HomeHub5 which has the wireless switched off so the TC is my router and HH5 is effectively just a modem

This is not correct.  Simply turning off the wireless on HH5 does not make it a modem. The HH5 is still acting as a wired router for the network.

Since the HH5 is providing routing services for the network, the TC needs to be in Off (Bridge Mode) to work correctly with the HH5.

If you tried to open ports on the TC, then you must have changed the TC to act as a router......and now you likely have two routers in conflict with each other fighting to control the network.  You only want one device on a network acting as a router......not two.

So, before you do anything else, I suggest that you get the HH5 and TC set up correctly.

I have followed instructions from various places to setup my network such that my TC is my only router.

I doubt that the TC is really acting as the router for your network. It might be providing a wireless network signal, but that does not necessarily mean that it is the main router for the network. 

We need to check some settings on the TC, but don't know what device that you use to administer the TC......a Mac, a PC, or an iPhone / iPad.

If you use a Mac to administer the TC, we need to know the operating system that it is running. Click on the Apple icon in the upper left corner of the screen and then click About This Mac.....then, post back with the OS X Version number that you see there.

Bob reminded me of all my setup iterations I went through to a TC. When he mentioned the key word (bridge mode) that was where I was the most successful. The only difference is that I setup my main incoming router (modem) to bridge mode and left my TC as the IP distributer. This effectively left my main incoming modem as a pass-through if you will. I'm not sure about the main incoming hub you're mentioning however, you need to access that hubs configuration to change it. Check with your provider if your not sure.

My TC is in bridge mode and everything else works fine.

The TC cannot perform as a router when it is set up in Bridge Mode (routing is turned off in Bridge Mode), so the HH5 is acting as the (wired) router for your network.

Even though the TC is in Bridge Mode, it can perform as a wireless access point and create a wireless network signal....which appears to be the way that you have your network set up.

So, to summarize, in your current network setup the HH5 is the wired router for the network and the TC is a 'bridge" acting as a wireless access point providing the wireless signal for your network.

You mentioned that you tried to "open ports" in your previous post. Since the TC is in Bridge Mode....and it is impossible to "open ports" on the TC when it is in Bridge Mode....you must have tried to "open ports" on the HH5, correct?  Can you provide more details on exactly what you did to the HH5?

I have been trying to do this on the TC which is why it won't work!!!

I'm still confused about this, since there are not even any settings to allow you to try this.  Do you mean to say that you could not find the port settings on the TC, or did you perhaps change the TC to DHCP and NAT router mode and then try to change things that way?

It is important that we understand what you might have done, since that will affect everything else that follows.

Do I have the best setup as described to create a strong wireless network?

Yes, although you could turn the wireless back on at the HH5 if you want to have a "guest" network or something like that.

I have heard that the TC is a better wireless access point (now i know what i'm talking about) than most general routers distributed by ISP's

That is correct in most cases.

Then, how would I set it up for the network suggest?  i.e. three ethernet wired devices and then wireless access for the rest.

You are basically already set up. Connect Ethernet devices to the LAN <--> ports on the TC.  Add an Ethernet switch to the TC if you need more Ethernet ports. The TC wireless provides the wireless signal for the network.

Connect one device at a time and get that working correctly before you try to add another device. The Apple TV will work much better if you can connect an Ethernet cable from the TC to the Apple TV.

I changed the TC to DHCP and NAT mode

You cannot do this. Bridge Mode is the correct setting for the TC.  When you did try to set up the TC to use DHCP and NAT, I'm sure you saw a message about a Double NAT error. That is the kiss of death with Xbox.

Since the TC is in Bridge Mode, you will have to make any port setting changes that the Xbox might require on the HH5. Get with the support folks for the HH5  to let them know what you want to do.

The TC in Bridge Mode is passive. It will simply pass through the new settings that it receives from the HH5.

the Apple TV won't connect to the network via ethernet either....).

You need to get into the Setup of the AppleTV to tell it that  you want to connect using Ethernet. It still thinks that it should connect using wireless.

How to restart your Apple TV - Apple Support

Just a suggestion. Per my previous post. If your going to go through the trouble finding out how to access and manage your HH5 consider making it the bridge mode and letting the TC do the routing.That solved a lot of my fiddling around trying to tweak another router. Apple routing, simple, easy to access and manage. Get into your HH5, bridge it, get out. Let it be a dumb box that just supplies you an IP Address to the outside world. Happy routing.

Good thought, but you might not be aware that if you "bridge" the HH5, the Time Capsule will then have to provide the PPPoE connection service.

That would normally not be a problem, except the U.K. uses PPPoA authentication, which the Apple routers do not support.

Well that's very interesting. Wasn't even thinking UK. I'm glad I followed this post because I learned something. I always challenge myself to keep learning more about networking and this is something I'll remember. I hope you're able to help the chap out.

Home Hub is the name of the modem/router that BT (British Telephone) supplies to their customers, so there was a clue in the original post. But, it's always possible that BT has made a very recent change to using fibre for some of their service. The HH5 has a regular phone jack for the Internet connection, so it is likely using PPPoA credentials to connect.