After spending 6 hours on this the other day with various support people at Apple the issue IS NOT resolved.
Here's what I know:
If I try and sign in to iTunes at any PC on our home Wifi I get the "We could not complete your iTunes Store Request. The iTunes Store is temporarily unavailable. Please try later."
If I enter my password deliberately wrong I get a different message so authentication is partially working.
The rest of my family can sign in to iTunes at any of 4 PC's in the house (indluding mine).
If I try to sign in to iTunes when connected to 3G (Samba UK) rather than Wifi (Virgin media) then I can sign in. How does this work?
I had a long (2 hour) phone call with senior apple tech support and it is a mystery to them too.
If there was an issue with our network then no-one would be able to sign in.
The only way I can explain this is that my account is on a different server and the path across the internet is somehow different and causing issues (number of hops vs TTL?) between Virgin media and Samba.
Anyone else got a clue why this is so (though at least I have a workaround now, but it is still broken).
Not planning on ringing again for a few weeks unless I really need to as support is not douby very busy after the release of iOS 7 & iPhone 5c/5s.