Sally-Anne, I'm afraid I don't agree. If you live outside Bucks and your child passes the 12+ AND you apply for a Grammar school which has places in year 8, your child HAS TO be admitted. As I understand it, both Burnham Grammar and Sir Henry Floyd are very likely to have places free in year 8.
However, Guest, the places are still allocated according to distance from school gates! The child only HAS to be admitted provided the place isn't given to someone who lives closer to the school!!
Hence, it remains a lottery, and my advice to Jenny stands - if you want to have any chance of a place, you need to be as close as possible to your preferred school. There are a small number of "pockets", particularly on the Bucks/Berks border where a child from another county would gain a place on the distance rule, but the same does not apply on the Bucks/Herts border, nor the Bucks/Northants border.
The following quote is from the Bucks 12+ document:
There are only a very limited number of spaces in grammar schools and this changes over time. So, there can be no guarantee of a grammar school place for a child who qualifies through LTP, as vacancies are usually only as a result of another child leaving one of the grammar schools. Only a small number of pupils who qualify though the Late Transfer Process each year are offered a grammar school place.
There are 7 Bucks Grammar Schools with places in year 8 at the present time.