Ignore comments from those who would never consider private education on principle. That sounds harsh but in terms of you getting the job and doing it well, they are not your target audience.
Firstly, I'd say know your market. Is the school in an area already saturated with indie schools? Or one where the state options are considered dire? Your approach will differ upon the answer to these. If local schools are considered very good then your job will be harder and you'll need a different approach.
Are there any high charging, well-heeled day nurseries in the area? If so, it would be worth your while targetting there. A leaflet drop or even holding a seminar here explaining how sch fees are likely to be less than they are currently paying in daycare may help.
If the local primaries are very good you need to emphasis what you offer above and beyond. How does your sport and music provision compare? At primary level in state schools, kids will average 2x45min sessions of PE and often this doesn't always happen and is the first to go to allow for assembly/show practice.
Can you emphasise small class sizes? What about extra-curricular? Middle class parents love pictures of things like infant children pond dipping and collecting things in the woods. What are your school grounds like? If you go 0-18 I'm imagining they're excellent so make the most of them.
Perhaps suggest an infant 'outdoor' kit. (one of the things that convinced me was seeing how they had all in one kagool type things in school colours which the infants wore to go walking/collecting in the woods which are part of the school grounds.)
Lots of info and pictures showing us how subjects such as history were 'brought alive' with elaborate displays, artefacts and visitors who came 'in character' as people such as Henry VIII. It wasn't just talk either and my kids love this stuff!