Details of the section where you need a permit are here ...
http://democracy.kent.gov.uk/mgIssue...aspx?IId=15321
... and this is the application form for the permit (took only a few days to come through).
https://shareweb.kent.gov.uk/Documen...pplication.pdf
The image shows our route, we did lots of shorter lanes as well, but this is the main section. The "closed" section is marked by the red flags.