Timber batten (Downend BS16)

I have a baby gate to put up but need a piece of wood to attach it to the newel post. I need a piece of wood at least 83 cm long and between 4 and 7 cm wide and thick enough to support the gate's hinges.
I do not have transport so I an only collect within easy walking distance of Staple Hill, Downend, Fishponds, Mangotsfield or Kingston bus stops ie. Bus routes 7, 49, 49x and 19. Thanks 🙏