I'm not a CP mum, but I am a Lambeth parent with long experience of the SEN team. Am I right in thinking you are applying for a reception start in 2020?
If your son is currently in an early years setting they should be able to apply on your/your sons' behalf for an EHCP needs assessment. That can help with the process (although I did a parental application myself, it seems school ones get treated as more 'official').
There is no 'kick ass' person in the SEND team as they are all massively overstretched, but the IASS service (Chris White firstname.lastname@example.org
) can help you navigate the system. Lambeth Parent Forum and Family Action can both give you advice and support that can help you through the process and information about drop ins with the SEND team where you can get direct access to a member of the team and that often helps push things along.
If you sent in your application for an EHCP needs assessment via email, resend it, point out the date that you originally sent it and politely remind them of the six week statutory deadline for them to make a decision whether or not to assess. Sounding like you know the law often helps.