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Primary applications have to be made by 15 January normally. You should apply at your old address so you have an on time application and also in case your move falls through (plus becuase if you obtain a place at a popular school then you have something your LA will want to reallocate so may be more interested in helping you).
Late applications that are due to house moves and other "valid reasons" are accepted up to 15 February, so if you were to have an offer accepted on a house before then you can change your application and still be treated as being on time. Or if this is still not possible at that stage, you can change your application after then but you will not be considered until after on time applications have been dealt with.
The policy that sets this out on SCC's website is here
SCC admissions coordination
Also the following doc shows actual offers of schools in Mole Valley for 2012 - so gives you an idea of where people lived and got in from this year. Several of the Dorking schools have faith based criteria, so if your child is baptised or you live in the correct parish they are higher priority. So it is important to know how this impacts you.
SCC 2012 Mole Valey Primary Allocations
I don't live in Dorking so no local knowledge but from the looks of things from SCC figures the schools in Dorking appear to be full at the initial application stage. However, if you do end up applying later than 15 Feb, if you do this before approx the end of April then the wait list will not have been allocated to yet. So you would join the wait list in the order of admissions priority, not based on the timing of your application. While the schools look full initially, most schools will have 1 or 2 families move/decide to go private so there will generally be 1 or more places allocated from the waiting list.
Your best chance if you are late in the process is to aim to live near (and meet the admissions criteria) of a larger school as the probability of a place being declined is higher there - so from the looks of things that would be St Paul's CoE as it is 2 form entry. The distance figure for this is for those living outside the parish - if you lived in the parish this year as a late applicant then you would be 1st on wait list.
One more thing you could do is to call SCC admissions team now. Explain you are thinking of moving to Dorking and will need a reception place and ask where there are still places available. Would give you a feel for what would have happened this year if you were a really late applicant, and so give you an idea of the worst case outcome.