Hi, gosh it does sound like you've a lot to think about there! Must be very stressful. I'm sure it will all fall into place eventually :).
Re schools... Whether or not your twins can defer a year will probably depend on when their birthdays fall. Personally i wouldn't be keen on that idea for several reasons including those you mention. I also wouldn't want to be paying for private if you can't really afford it - it's a huge commitment.
I would suggest calling the primary admissions team of your chosen borough (once you know which this is!) as only they can confirm the best approach in your situation. They are the ones who control how places are allocated.
Yes, it is really a case of where there is a space, but this doesn't necessarily mean it will be a bad school. Most schools are fully subscribed these days, even those which aren't everyone's first choice, so it's unusual for there to be many places remaining after offer day. Any that are left will usually be needed by someone who hasn't been offered a place anywhere anyway.
In general, the fair access policy is something along the lines of they must offer a place within 2 miles / 45 mins travel - so they can by law effectively offer pretty much anything in the borough. I think they do genuinely try their best to match people with their closest schools and keep twins together wherever possible though. I have even heard of extra place being created for a second twin. Some councils (Bromley is one) won't process applications though until you are resident at your stated address and paying council tax and they have the evidence. They also usually have a time limit on finding you a place but this is measured in school days (term time) so you should apply as soon as you're able to stand the best chance of having a place at start of sep term.
When you move into a borough in-year you are usually added to a waiting list but given priority over others who already have a place somewhere regardless of distance. I believe same applies for reception applications after the deadline. You should check with the admissions team though.
If you are offered a place you should accept it regardless of what you think of the school as you can still opt to remain on waiting lists. Just be aware however (to set realistic expectations), that depending on various factors, including the number of people moving into the area, it may take years to be offered a place and it may never materialise.
On a more positive note however, Places may become available at any school, excellent ones included. As you are back in June this may work in your favour as you will have a couple of months over the summer where places may become available at your preferred schools. There is always a bit of a shakeout period over summer / start of term in reception too where people decline places for various reasons (house move, opting for private, taking up place elsewhere etc) and these places are offered to the next on the waiting list.
I guess the more decent schools there are around your chosen area then the greater chance you have of being happy with what you're offered, but unfortunately there's just no way of knowing what you will be offered until they actually offer you a place. Most primaries around Bromley are fine and I'm sure this is the case in surrey too. Try not to worry too much - and remember ofsted outstanding isn't the be all and end all where schools are concerned. Unless a school is rated unsatisfactory it should be doing most things right, although they do all have a different feel etc. Maybe you could try and visit a few schools to give you a feel for them. You can get all the govt stats and ofsted data online. The council website should also have a starting primary booklet which will tell you about all the schools and admissions. I'm sure you know all this but just in case! Once you have an address the council will be able to tell you where you are on the waiting list for particular school if you're hoping for specific ones.
It never does any harm to ensure you're happy with your closest school options (in terms of proximity as well as quality), but as you will have little control over the places available I wouldn't worry about being on the doorstep of specific ones - your house will cost you more and you may end up being disappointed. The area and commute are equally important too IMO.
Sorry that ended up bring quite long! Hope it helps.