We currently have Fibre with BT Halo 1 and can get a maximum of 34 Mbps (down) for the past few years.
Thankfully, we never dip below this speed.
However, is there a way to see if my area (ST19 9PN) is due a speed increase and if so, when?
The only speed increase will be when/if Openreach roll out full fibre FTTP to your location. Only Openreach will know when that will be.
Unless another provider such as Vigin, Gigaclear, County Broadband, etc. lay fibre in the street. But that would obviously require jumping ship.