Caught the source of these support calls
One of these calls got through to the elderly (gullible) father of a friend of mine. He ended up giving access (they come in via TeamViewer, whether it's installed before or not) and paid them for the 'service' on a continuous authority debit card billing. Particularly dangerous, as those go though even if you change bank accounts - they just follow the leader to the new one.
In this case, the company was hiding behind a .co.uk domain name that had been set to be anonymous from a Whois point of view (something that should only be available to private individuals). I complained to Nominet, who then exposed the Whois data. Maps back to one of two directors who have 12 companies registered at Companies House in Coventry, who use a UK Barclays account to receive funds and who have 600 telephone based staff in a call Centre in Kolkata, India. Then worked with Stevenage Trading Standards on the result.
There is little Talk Talk can do - they hop across multiple caller IDs (about 12,000 complaints down to two specific ones). If Talk Talks voice hardware can knock out calls based on the private Caller IDs (not the editable public ones), that would be a useful service to offer. Outside of that, it's awareness campaigns (as these support calls come from one of multiple pretend sources) and working with trading standards; the Stevenage ones have been brilliant in our case.