Looking at those Google results, it seems that these calls come from a sales company who are trying to get you to buy a new phone.
Like many call centres, this firm appear to be using an automated call system which dials hundreds of numbers at once. As soon as a call is answered, the system transfers it to a salesperson. If, however, all of the salespeople are already busy with other calls, the system simply hangs up the call. If the company has difficulty recruiting and retaining call centre staff, it's quite possible that the vast majority of calls dialled by their computer will be terminated as soon as they're answered.
You should be able to stop the calls by registering your phone number with the Telephone Preference Service. You can do this for both landline and mobile numbers. The service is free and you can register online, here:
http://www.tpsonline.org.uk/tps/
If your number is already registerd with TPS, still go to the above link and then click on 'Complaints'. Although the link says that TPS can't act regarding silent calls, this only means when you have no contact details for the firm. Report the call anyway, quoting the phone number and stating that it was apparently a failed sales call from COMMUNICATIONS DIRECT LIMITED
33 HEATHFIELD
SWANSEA
SA1 6HD.
Chris