This is primarily a community help and support forum so while Virgin Media can and do respond on here, it can take them upwards of a week to do so.
I'm not a Virgin Media employee but this is my take on the situation.
1. Pings and tracerts are inconclusive as it appears that the site is blocking ICMP echo responses. I have used an alternative tool called TCPing instead.
PS C:\Users\timdu> tcping www.slleisureandculture.co.uk
Probing 220.127.116.11:80/tcp - Port is open - time=94.389ms
Probing 18.104.22.168:80/tcp - Port is open - time=75.714ms
Probing 22.214.171.124:80/tcp - Port is open - time=61.153ms
Probing 126.96.36.199:80/tcp - Port is open - time=50.226ms
Ping statistics for 188.8.131.52:80
4 probes sent.
4 successful, 0 failed.
Approximate trip times in milli-seconds:
Minimum = 50.226ms, Maximum = 94.389ms, Average = 70.370ms
So it's not a general block against Virgin Media users
The fact that it's blocking you when you are in router mode, means that South Lanarkshire Leisure has decided to block your public IP address (you have a different public IP in modem mode).
Now because they are the ones blocking you - only they can remove that block. Which is why Virgin Media asked you to contact them directly. You can find your current public IP by simply entering IP into a Google search bar from your Virgin connection. Note that Virgin IP's
South Lanarkshire Leisure's headquarters number is Tel: 01698 476262 (Taken from their website)
Only use Helpful answer if your problems been solved.
What does traceroute show? I had an issue where a routing/peering issue blocked access to download.company.com though www.company.com worked OK. The issue was not on the VM network but VM needed to deal. Took some time to fix. traceroute was very odd with www showing one route and download something completely different though IP's where adjacent and notes showed them both to same "location".
That said because you can access in modem mode the supplier may have a block on the IP of your Shub. You could login to Shub to get external IP and if different from IP that was assigned to PC in modem mode ask the supplier.
If you do what you've always done, you'll get what you've always got. Jim Elliot
I work for Virgin Media but respond here on an individual basis. No comment or assistance offered is done in any official capacity.