Watson, who has been a key figure in the campaign investigating phone-hacking at News International, made the call following the news that the Met hired former News of the World executive Neil Wallis as a comms adviser in 2009.
Watson told PRWeek: 'It strikes me that the Met needs to rebuild its credibility with all other news organisations and the new world of social media.
'An overhaul of its strategy would be timely and help a new commissioner signal a clean break with the past.'
Director of public affairs and internal comms Dick Fedorcio remains in his post, although he is forbidden from handling any external enquiries in relation to phonehacking and has been referred to the IPCC over the affair.
A source at the Met said that it 'remains to be seen' whether there would be significant changes to the Met's comms operation, but admitted that 'changes were an option on the table'.
It has also been revealed that ten of the 45 employees in the Met's department of public affairs have previously worked for News International. A Met spokesman told PRWeek that the ten were not 'high profile reporters' and half of them had worked for other newspapers as well.
Following the outrage over the appointment of Wallis, Met Police commissioner Sir Paul Stephenson and his assistant John Yates both tendered their resignations.
They have also been referred to the IPCC, along with Fedorcio.
The IPCC is looking into what areas the inquiry will cover, co-ordinating with the judicial inquiry being held by Lord Justice Leveson.
A spokesman for the IPCC said the Met would be free to carry out its own internal review while the IPCC review is ongoing.
In addition, HM Inspectorate of Constabulary is set to review alleged police corruption and relationships with the media.