Internet connection issue

[#1]

This has happened several times over the last few weeks...
I launch firefox and attempt to connect to a website such as bbc.co.uk.
The connection fails.
If I connect to my SpeedTouch router (via firefox), it tells me I am connected to the internet.
If I run the SpeedTouch internet connectivity checks, everything looks ok - I get green ticks against everything in the list:-
DSL
ATM
PPP
IP
Internet Connectivity to Gateways 195.166.128.195, 212.159.6.10 and 212.159.6.9
The only thing that seems to fix the problem is to resync the router - even though the ADSL connection is reported as ok.
When the system is in this 'connected' but 'unable to browse' state, I have also found that if I disconnect the internet via the SpeedTouch 'broadband connection' page, it will not reconnect until I resync the router.
Any idea what's going on here?

[#2]

If you're having to reboot the router to get connected it could point towards the router being faulty.
When it happens next time can you try a traceroute to a website like bbc.co.uk and then copy and paste the results?
https://support247webs.com/windows-traceroute/

[#3]

I'm not rebooting the router to fix the problem - I just initiate a DSL resync using the DMT tool (http://www.kitz.co.uk/routers/DMTv8.htm)
DMT doesn't indicate an ADSL connection issue when in this fault condition.
If the router were faulty, then I doubt I would be able to ping the Plusnet Gateways in this state (which I can do).

[#4]

Another thing I've noticed over the last few weeks is that google searches can sometimes take a very long time. i.e. minutes while firefox displays 'Connecting'. It used to be that google searches were very quick, taking only seconds.

While the google firefox tab is displaying 'connecting', I can usually connect to another URL on another tab.

If I try ping or tracert to www.google.co.uk, that seems reasonably quick.

Has something changed with the google server?