Post pregnancy cervical smear test (UK)

Laurie • Our beautiful baby born 18th Nov 2015. Baby #1.💙💙💙
So in the UK you have to be over 24 to receive a cervical cancer smear test.
I thought that you had to have one free giving birth regardless of age, but my dr didn't even mention it at my 6 week check up until I brought it up and even then she was quite dismissive and told me to try and book in 3 months and now I'm worried they'll turn me away! 
Has anyone under 24 from the UK had a post pregnancy smear or did they refuse?