I don't want to add to the stress you've already experiencing but thought I'd share what I know from the situation we were in last year... we're in Lewisham which calculates home to school distance along a straight line, so different from Wandsworth. We applied for DD to start Reception at the school where I teach (and she attended nursery although neither points have any bearing) which was approx. 650m away. We didn't get a place there or at any of the other schools we listed but were allocated one 2.8 miles away in the opposite direction at a school that had been expanded, eventually permanently although their 2010 Reception intake will be smaller because of building work and a lack of spare space on site.
The 2.8 miles is two buses from here and because of the route crossing railway lines was more convoluted than some. My husband and I are teachers, he takes the car as he teaches further afield and I walk. The school DD was allocated had no before or after school provision and no local childminders did drop-offs etc. so far away (no real surprise but we did check!). We declined this place and initially said we would be reserving the right to postpone her start in Reception until she reached Statutory School Age (Jan 2010). The admissions person got all het up and admitted that wasn't an option on their form!?! I suggested she record it as home-schooling for the time being. Meanwhile we asked to be added to the waiting lists of my school and a very unpopular but very local school.
However, as a back-up we'd also applied for a school out of borough but opposite where my husband teaches knowing that it had before and after school provision so if absolutely necessary she could travel with him (he leaves at 0630) each day. It wasn't what we wanted long-term but if it meant that we could both continue to work (part-time) we'd have done it as the other option was for me to give up work to spend 3-4 hours walking to and from the allocated school each day (prams on buses aren't terribly welcome and DD2 was 13 weeks old when DD1 started Reception). Bizarrely we were offered a place at this school; 5+ miles away and accepted it.
A few weeks later we were also offered a place at the local but unpopular school so accepted that and decined the out-of-borough place. DD1 started Reception and had a very happy term there until Christmas... by January she'd moved to the top of the waiting list for my school and a vacancy arose. She re-started at my school in January. For various reasons (people moving out of London, a child's parents deciding to home-school and another being offered a place at a 'special school') other vacancies have come up too and been filled immediately.
What I'm trying to say is that this will feel terrible at the moment and it is but there is a lot of mobility in urban schools (as a teacher I have never in 10 years started and finished the academic year with the same group of children) and chances are you will end up with something in the short-term and a more preferable something in the long-term.
Re: bulge classes, there will have been a thorough feasibility study conducted to identify which schools have the capacity to take a bulge class in any one year. Some schools may be permanently expanded but the costs of the rebuild that may be necessary are often considered prohibitive. Some schools may be able to accommodate a temporary/demountable classroom which will be used year on year (for Reception 2009, Y1 2010, Y2 2011 etc.) but having one of these will often reduce playground space. School halls may be able, at a squeeze, to fit in an additional 30 children but that may mean that parents aren't able to come and watch class assemblies because there is no space to accommodate them, dining halls and kitchen capacity mightn't be large enough to get everyone through in a sensible time, the areas available for breakfast/after-school clubs won't suddenly expand regardless of greater need for the provision plus there is bound to be a knock-on effect in later years when siblings of the 'bulge' intake are given priority over new entrants who live on the doorstep of the school etc. etc. Physically many schools will not be able to cope with a permanent expansion because it's not just about 30 5-year-olds because they grow up and need more space.
Schools are directed to take on a bulge class, the Governors will submit a response to the proposal but if the LA needs the spaces in that area and deems the school able to cope then there is little the school can do but get on with it. Lewisham has announced somewhere in the region of 12/13 bulge classes for this September but most of tose schools would not be able to accommodate an additional intake of 30 permanently because the space just isn't available. Next year it is likely to be a different 12 primary schools that are directed to accommodate additional children and this will continue until more schools are built/rebuilt.
I do sympathise with you and would encourage you to look further afield for a place but would also urge you to think carefully about how you'd feel if your local schools were pushed to take yet another 30 children and, as a result parents couldn't see their 5-year-old in the nativity because the hall was dangerously overcrowded or your 5-year-old regularly came home hungry because lunch had to be gobbled so 400 children could be fed between 1200 and 1310.... that's not something to bring up at appeal but perhaps something to bear in mind if you do get involved in local action to expand schools.
Sorry for extremely long post.