When I purchased my last boat I paid for a specialist surveyor I knew to come up from the Solent. It was slightly more expensive due to travelling, but worth it for his knowledge.
A lot of Hoo Ness Yacht Club members use Alf Cackett, who is based in Brasted, Kent. http://www.marinesurveyorskent.co.uk/ He is also the only surveyor mentioned on the Hoo Ness web site.
Alf is probably the most local and does lots of surveys on the Medway.
Mandy Bruce (www.magellanyachtsurveys.co.uk) has been very helpful in the past. I must point out that I've never asked her to do a full survey, but she has helped us with specific questions being very fast and friendly.
We had our insurance survey done by Robert Bingham Mobile Number 07881 611157 Cost us £300 for a 10m yacht. Chatham, unlike Gillingham don't mind who you have work on your boat.