The offical policy from Essex CC is:
Applications received after the published closing date will be treated as late applications unless there is evidence or you provide evidence to show that the application could not reasonably have been made on time. A new preference or change in the order of preferences will not be accepted after the closing date unless the circumstances are deemed to be exceptional. Late applications will be given a lower priority and will be dealt with after all on time applications in the first round of offers on 1 March 2012. Where a school is oversubscribed late applications will be refused and ranked according to the admission criteria on any waiting list held for the particular school. All late applications will be considered by an LA panel of officers to ascertain whether exceptional circumstances for late submission exist. Where that is deemed to be the case the application will be treated as ‘on time’.
Where a school is oversubscribed late applications received after the first round of offers on 1 March 2012 will be refused and ranked according to the admission criteria on a waiting list held for the particular school.
However as you live out of Essex you have presumably applied via your local CC so any change of priority at this stage would need to be done via them rather than ECC.