Ok so now I am really getting confused. I am leaving TEl Aviv and my Visa for China is in my British Passport. Am I right in thinking it's okay to leave Israel on my Israeli passport and then arrive in China and present them with my British Passport?
And of course we are going through Frankfurt. Do I have to show any passport there and if so which one?? Sorry if I am panicking but this is a bit more complicated than my regular 2 week trip abroad.

It's fairly simple. The rule of thumb is that you use the same passport to exit a country as you did to enter it. So, you should exit Israel on the same passport you entered the country, and then use your British passport to enter China.
As a rule (and in some countries as the
law) if you enter or leave one of the countries where you have citizenship (in your case the UK or Israel), you should use that country's passport. I presume you last entered israel using the Israeli passport.
Hope this makes things clear for you.