For any Accredited psychotherapist post you will need to do an Experimental course, not necessarily a Masters but another course after your BA.
Get on to the these 2 NHS recognised accreditation bodies for definitive career routes.
TBACP trains counsellors and psychotherapists
The UKCP trains psychotherapists.
There are Masters degrees around for psychotherapy i believe a general experiential Masters training would then require some exyra childhood pg diploma, (check with the above bodies as this may have evolved), tjere may well be specific childhood psych Masters qualifying degrees now.
But generally, no with A BA, unless it is an fill on Experiential psychotherapydegree, yoi cannot go practice directly afterwards.
Hooe thos ingo helps, the governing bodies are the place to get the thourough advice, esp if you wish to Practice NHS .
Otherwise check other psychotherapy bodies for private (more expensive too) therapist training advice.
Good luck.