Although the 30% private school number is no doubt still too high, I do not think 7% is the "right" number. As i understand it, the % at private school is closer to 20% for sixth form, so assuming the numbers are derived from the school they are at at the time of application, you would expect the number to be higher than 7% private school as a starting point.
Also, it is not really comparing like with like in that far more private schools are academically selective so will tend to have a greater % of pupils who are capable of getting very high grades. Of course, the fact they are at private schools will make it far easier for them to achieve their potential (so this needs to be factored in), but it is still relevant. In comparing the GCSE results of a grammar school to a comp, for example, i don't think a straight comparison of % of 7s to 9s would be a fair reflection on the performance of the comp in determining where bright pupils get a better outcome - i think it is more appropriate to compare the performance of the grammar with the top (say) 20% of the comp cohort. I think the comparison here is somewhat similar (to a lesser extent).
There are obviously all sorts of other things that distort the comparison both ways - pupils who move from private to state for sixth form, high-performing selective state grammar schools and sixth form colleges, pupils at private schools on bursaries etc.
In summary, i don't think it is a simple as saying that the "right" outcome is that 7%% of Oxbridge applicants should come from private schools. That is not to say i think 30% is the right number either and more progress is no doubt required, but it is at least progress in the right direction.
I have a DD waiting to hear from C although she is not at all optimistic, and happy with both the offers she already has (but keen to hear from the other two, particularly Durham!). She is at private school. DH and I both went to Oxbridge, both first generation in our families to go to uni, I am state educated and DH went to private school on a bursary FWIW.
DD's private school (academically selective but not at the Westminster/St Pauls/NLCS/City level) got a higher % of O offers yesterday than expected (no noticeable reduction and an increase on last year which was lower than normal). However, far more applied to C, so the combined numbers may be more telling. Also a higher % applied than normal (maybe because overall GCSE grades will have been higher due to teacher assessed grades, making some more ambitious in uni choices). Interesting to know if the total number of applicants increased significantly
It would also be interesting to hear feedback on how the likes of Westminster etc. have done.