I spoke to my HV when DS had speech problems (which are completely gone 1 year later!). Do the nursery think there is a problem too? I suppose at four the HV isn't really involved too much so the GP could refer her.
You can go through all the people mentioned here, but bear in mind some may try to fob you off (eg GP). Insist-it is your right.
Some departments allow parents to refer their own children or for adults to refer themselves. We do and are very proud of this fact. Ring the department directly and ask-if they accept, at least you know that your case hasn't been sittiung, pending, on someone's desk for weeks!
We wrote directly to the Director of Education for our Borough. We said our DS (who was 1 at the time, he's profoundly deaf and wears hearing aids) has already started private speech therapy lessons which cost £40 an hour (they've become much more expensive since then) and that we are happy to continue with this arrangement until they get staff sorted out but will be expecting a repayment of our costs. Incredibly, we received a quick reply with an appointment with a speech therapist. He's had regular, weekly, speech therapy sessions ever since.
Our HV, teacher of the deaf etc. all knew about DS's deafness and need for speech therapy but they also knew of speech therapy staff shortages in our Borough so didn't do anything about it (probably unwilling to further burden their colleagues or create difficulties for them, I don't know). So we wrote directly. (We also wrote to our MP, useless guy, wishy-washy.)