Found the problem. A process with the name of MobileBroadband.exe, courtesy of a Vodafone dongle.
I still don't really understand why, because the Vodafone's software has been there all along while I have been using the laptop, but I have recently come back to the UK after a 2 month absence, so perhaps it was one of their updates to 'give me a better service'.
Anyway, job done. Thank you for all your suggestions.