If your struggle with voice is because of pitch, that can be resolved with glottoplasty. You dont have to go to Korea or dr. Haben for this.. There should be more than enough ENT doctors who specialize in phonosurgery in UK, that you shouldnt have trouble finding one who performs glottoplasty on regular basis. This should be covered by NHS.
Reality is most trans women need facial feminization surgery in order to pass (by that I mean not getting clocked). Not everybody needs full facial transformation, or same amount. Its very individual. We learn from a very early age to distinguish between masculine and feminine face, even if the difference is very slight and even if we are not consciously knowledgeable about any of facial features or gender markers. Our attention always goes to eyes, and eye expression due to underlying orbital bone structure and shape is the most deciding factor to whether we recognize that persons face as masculine or feminine. Make-up can cover and change some of that, but some people will still instantly notice the difference.
Im sorry you have to deal with some ignorant people.