It could be that your laptops have IPv6 selected. Try disconnecting it as follows:
In the search field type.ncpa.cpl and press enter.
In the new window right click on your wireless network connection and select properties
In “This connection uses the following items” section remove the tick beside Internet Protocol Version 6 (TCP/IPv6) then press OK
Left click on Internet Protocol IPv4, click properties . Check the options to obtain IP address and DNS server address automatically.
Once done try and connect to internet.
It is odd that two of your computers have the problem and the phones and tablet don't. That would tend to rule out the router being the problem.
You could try resetting TCP/IP on the computers to see if it helps.
Open a command prompt by clicking Start and then type cmd in the Search programs and files box.
Under Programs, right-click the CMD.exe icon, and then click Run as administrator.
When the User Account Control box appears, click Yes.
Type the fllowing commands into an elevated command prompt one at a time, hit enter after each one then reboot the system.
netsh winsock reset
netsh int ip reset
Presumably you will have factory reset the router and set it up again?
I would agree that it appears to be a router problem except that your other devices are working correctly.
I don't have any knowledge of that router so can not advise what the settings should be other than the username and password for BT which you already know but as far as I am aware it should be more or less plug and play.
Does this happen on both wireless and wired connections?
What browser are you using?
Have you tried another browser?
Does it happen with HTTPS sites and non HTTPS sites?
Do you have any banking software such as Trusteer Rapport installed?
Make sure that you are not set to connect through a proxy.
Go to Start > Control Panel> Internet Options > Connections > LAN Settings > tick Automatically Detect Settings.
I am at a loss because of the conflicting information. Router works OK with mobile devices but not laptops this would tend to point to laptop problem. Laptops work OK on HH5 which would point to router problem.
Did you install any software that came with the router?
There was a few posts on line about the router QOS setting WWW Wifi enable multi media being ticked when it should be unticked but this apparently only affects wireless connections so it might be worth checking.
You might find as the evening goes on somebody with the same or similar router will read your post and post what settings they are using. Meanwhile do you have a friend that could try using their laptop to connect to the router to see if the problem occurs with them.