Very simple really - just setup IE to point to a proxsy server.
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In Internet Explorer, select 'Tools', then 'Internet Options', then 'Connections' and finally 'LAN settings'.
Please make sure 'Use a proxy server for your LAN' is checked,
In the 'Address' box, please type 'webcache.virginmedia.com' and enter '8080' for the 'Port' setting.
Ensure 'Bypass proxy server for local addresses' is unchecked.
Please 'OK' settings and Apply.
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And that was it- IE was able to connect to the site.
What I wan't expecting was that Firefox and Chrome were also then able to connect.
Then I booted into Ubuntu (since IE isn't on Ubuntu for some reason) and both FireFox and Chrome were also able to connect.
The only thing I can think of was that one of Virgin Medias servers had decided that a particular route was my preferred solution, so I thought I would compare a tracert I took earlier with a fresh one - and sure enough there were some differences* in the route that my traffic took in the Virgin Media network.
So there you go - having problems connecting to The national lottery website - set up your proxy server as detailed above.
Simple really I guess, though of course there was no way of knowing this until I kicked up a fuss and someone looked at the issue.
*if you care:
Here is the route when I was being refused access
2 7 ms 5 ms 5 ms watf-core-1a-ae1-2985.network.
3 6 ms 6 ms 7 ms brnt-bb-1a-ge-320-0.network.
4 9 ms 9 ms 11 ms nrth-bb-1b-as4-0.network.
5 11 ms 72 ms 10 ms tele-ic-4-ae0-0.network.
6 10 ms 11 ms 11 ms ldn-b4-link.telia.net [213.248.70.29]
7 136 ms 28 ms 10 ms ldn-bb1-link.telia.net [80.91.246.144]
8 87 ms 85 ms 85 ms ash-bb1-link.telia.net [80.91.251.207]
9 101 ms 102 ms 100 ms atl-bb1-link.telia.net [80.91.247.173]
10 115 ms 113 ms 113 ms mai-b1-link.telia.net [80.91.252.58]
11 115 ms 115 ms 115 ms asurnet-ic-134141-mai-b1.c.
12 120 ms 118 ms 121 ms tengige2-1.usa.nmi-edge05.
13 132 ms 131 ms 159 ms 63.245.69.190
14 * * * Request timed out.
15 126 ms 125 ms 123 ms 24.244.158.2
16 133 ms 142 ms 142 ms 208-87-34-15.securehost.
Here is a traceroute when working config:
2 7 ms 7 ms 16 ms watf-core-1a-ae1-2986.network.
3 7 ms 6 ms 14 ms brnt-bb-1a-ge-320-0.network.
4 63 ms 61 ms 61 ms so-10-3-0-xcr1.lnd.cw.net [195.2.9.149]
5 135 ms 167 ms 131 ms xe-5-3-0-xcr1.nyk.cw.net [195.2.25.197]
6 140 ms 144 ms 141 ms xe-0-0-0-xcr1.ash.cw.net [195.2.21.182]
7 103 ms 94 ms 95 ms equinix-ash.epoch.net [206.223.115.52]
8 167 ms 167 ms 168 ms ae3-10.c01.ash.bb.
9 96 ms 95 ms 95 ms ae8-0.asbnvacz-mxc2.bb.
10 167 ms 167 ms 167 ms ae3-0.lsancagb-mxc2.bb.
11 171 ms 167 ms 167 ms ge-0-1-0-0.c00.lax.bb.
12 178 ms 171 ms 167 ms gig1-1.e40.lax.bb.
13 176 ms * 175 ms 209-101-27-70.lax-e100.cust.
14 176 ms 169 ms 165 ms whatismyipaddress.com [66.80.82.69]