The Information Commission's Office (ICO) had more than 3,600 complaints about automated calls in September - a five-year high and nearly three times the number it had in July.
But it suspects millions of people are getting these calls and told BBC Radio 4's You and Yours it was "deeply concerned" by the sharp rise.
The ICO advises people to ignore calls from numbers they don't recognise, and to block and report any suspicious calls to the watchdog.
The automated calls typically come from what appears to be a UK mobile number.
Some of the recorded messages mention an offer of part-time work.