Your public IP addy is assigned to you by BT. It tends to be sticky in that it doesn't often change when the router resyncs but it could do. BT has pools of these IP addys to hand out to its users upon connection. One of which is:
I'm not convinced that ones starting 88. are BT's but if you post the 1st 2 parts I can find the pool (but not your individual addy, be assured).
Your public IP has absolutely no connection with your internal IPs of your devices which are by default with a HH are of the form 192.168.1.n. They are hidden from the Net & you can change your DHCP IP range willy-nilly w/out it affecting your public IP.
Access attempts are a fact of life when connected to the Internet, especially an IPv4 address. Over the last two days my router has blocked 865 access attempts. All this means is the router is doing it's job. So what was 'hacked' the router (doubtful) or your PC?
The Hubs have proven to be unaffected by the recent router hacks so it would be interesting if you could give a little more detail of the 'hack'.
Are you certain that the suspect 'hack' is not the BT remote administration. EG: TR069.
You can try disconnecting using the disconnect option on the Internet section of the hub menu. This drops the session while still maintaining synch.
Then click re-connect again, and you should find that your public IP address has changed, that will always be the same as your broadband network IP address.
The only time that was not the case, was when BT were trialling CG-NAT, so maybe that was what you were seeing?
CG-NAT is no longer used by BT Broadband.
Yes, 22.214.171.124 - 126.96.36.199 is 1 of BT's IP pools. You said '88' earlier. That's why I couldn't find it.
Why are you bothering to change your Default gateway IP to 172.16.1*.** from the default 192.168.1.254? It is not protecting you from hacking & attacks.
Your public IP is your broadband network IP always by definition.
I suspect the Default gateway 172.16.1*.** mentioned is actualy inside the BT natwork, IE: WAN side rather than the LAN gateway address.