I would take a very good look at the availability of places in the schools you like.
I heard of a London case where a short move put the family in a new LA who were more penny pinching and promptly said that dc did not have as many needs as the parents said, and could go to one of their schools with much less provision.
Kent does have a reputation for very vague statements, and fighting against expensive placements.
That said I have seen one or two Kent special schools - all secondary I'm afraid - and been really quite impressed with what was on offer.
So be VERY clear on what Kent are agreeing to before venturing out of your London School. eg If you want speech and language therapy I would make sure it is delivered by an in-house SALT rather than an NHS visiting one and the statement gives the precise number of hours per week and says that it is with a qualified SALT etc.
You could be lucky, and see and be accepted by a wonderful school, so don't let me dash all your hopes. It is certainly easier with dcs who meet the 'severe' criteria as there is less room to argue.
Sorry not to be the bearer of better tidings, but their reputation for generous statements is not good.