You ought to check the success rate for appeals at the schools you're interested in. It can be difficult to win an appeal at some Essex schools - presumably because they are heavily oversubscribed.
Some of the Essex regulars may be able to tell you - or you have a legal right to get this information direct from the admission authority. See: http://www.elevenplusexams.co.uk/appeals/general#a39
For advice about how to appeal, see:http://www.elevenplusexams.co.uk/appeal ... cation#b11http://www.elevenplusexams.co.uk/appeal ... -school#c2
As a rule of thumb, the further away from the required score, the harder an appeal becomes.
If you talk to a headteacher, it should probably be to the head of your present school - you need to know how supportive they will be if you decide to appeal.