You need to book it seperately and dont even entertain packages.
Look at Kayak for flights. It will allow you to set up daily emails telling you your flight date options prices - and provide a little chart telling you if prices have dropped or risen since you started looking. Book when you see a good price.
Not sticking to 7 or 14 days will help. Travel out on a Thursday come back on a Tuesday for example (12 nights). You need to do alot of playing with dates and see what offers you the best deals.
If going for longer than a week then consider indirect flights. £700 odd for direct can become £350/450 each indirect. We have done this on longer trips and with small kids. Its not as horrendous as first thought but not as easy as direct but the saving financially can be huge 50% and even more. We made it part of our holiday and accepted the fact we would be at X airport for X hours and included in our costings a nice family sit down meal in an airport restaurant (not McDs) so we knew it would pass and hour or 2. If you consider this option I would not always go for the shortest stopover - because where ever you land first in the USA will be where you need to clear immigration - which can take hours (on a bad day). Much as a 1 or 2 hour stopover may seem ideal, by the time you as a family have all gone to the loo,cleared immigration and gone through security for your connecting flight - 2 hours can fly by - so be realistic if doing connections about how long you may need. It becomes stresdsful if its too short, more so imo than a long stopover where you can fill the time with meals and shops and its a time for little ones to stretch their legs a bit after the long flight over from the UK.
Shop around in the same way for accommodation.
Dont book disney accommodation. Lovely that it is - you will end up eating on site which is not cheap. Dont bother with a villa - you will need car hire and parking fees at the parks everyday (great that car hire is, its a cost that can be cut if looking to cut costs). Also with Villas you will be paying for pool heating in Oct ontop of the villa cost. The best option imo is a condo off site but close by to the parks. Condos offer everything a villa does (full kitchens,laundry facilities and communal free pool) 2 bathrooms even - which if a larger family like yours is trying to get out the door and into the parks early in the day will be a requirement.
International Drive is probably one of the cheapest areas to stay and has the Itrolley to the parks which is cheap to use (if not hiring a car) but I prefer Lake Beuna Vista. Some Condos etc provide free shuttles to the parks etc. Its not as flexible as having your own transport but its FREE and once in any Disney area you can use Disney Transport between parks. Alot of places also have free transport to Universal and Seaworld etc but you have to fit in with the bus timetables. Staying off site means you as a family may be able to eat out cheaply and not be restricted to the parks.
We have stayed here Blue Heron before and it was fab. Its in Lake Buena Vista so if you miss the free transport in the morning to any of the parks its cheap enough to get a taxi (if no car hire) - not every day but ok a few times. You can walk to DownTown Disney in 20 minutes, if you wanted and from there get the free Disney transport into any Disney Park. Its close to several eating places that are cheap like Cici Pizza and Golden Corral and a few shops etc. TBH - we dont eat in that much but brekkie we have in condo most days - something simple and quick like toast/cereal etc - over a 2 weeks holiday we may have brekkie out a few times but this alone must save us ££££ on eating out as a family every morning. Some mornings we even popped down to dunkin donuts for a truely un-healthy brekkie but with enough sugar to sustain stomping around the parks for a few hours until lunch.
We found the thing that works best for us is to hire a car for the first few days. This we have found works out the cheapest way to get from airport to condo and also a few trips to Walmart and the malls to stock up on food, drinks, packed lunches and a few cheap souveniers for the kids at the start of the holiday). The rest of the time we use the Condo free transport.
For accommodation spend hours trawling websites like Expedia,Traveocity, Travelsupermarket etc etc etc. You need to research and research and reasearch like mad - get to know which area would suit you best to stay in. Then heavily reseach certain accommodation that comes up - and then compare prices. A motel room would be the cheapest room option, but you will have little cooking facilities to even prep snack for brekkie etc and will be paying to eat and drink every meal out and about which may tot up the overall cost.
Start researching now - get a folder and a pad, make notes as you go. You can do it cheaper than initially thought but it involves time and effort. We went back in 2008 for 32 days and the whole holiday for 4 of us including spends came in at just under £5k including ultimate passes to all parks disney and universal, water parks, kennedy etc etc. That was our best deal ever - prices have gone up ALOT since then but bargains can be found if you put in the time.
Dont give up - you may find it is affordable but its not going to jump out easily at you - you need to make this a project if you want to do it cheaper. Good luck.