Gps will no longer usually refer on for removal of a mole that doesn't look suspicious because it's deemed cosmetic so not now something the NHS will cover.
OP says "but it's gradually becoming more fleshy and stands proud (it used to be quite flat),"
This to me sounds like a mole that is suspcious - I think an indicator of a need to get a mole checked out is any changes. OP apart from the cosmetic side, I think you should get it looked at by a dr (Whether that is your GP o privately) asap and agree with PP that this is not for a beauty clinic. You need to have it biopsied.
www.cancer.org/cancer/melanoma-skin-cancer/detection-diagnosis-staging/signs-and-symptoms.html says this:
The most important warning sign of melanoma is a new spot on the skin or a spot that is changing in size, shape, or color. Another important sign is a spot that looks different from all of the other spots on your skin (known as the ugly duckling sign). If you have one of these warning signs, have your skin checked by a doctor.
The ABCDE rule is another guide to the usual signs of melanoma. Be on the lookout and tell your doctor about spots that have any of the following features:
A is for Asymmetry: One half of a mole or birthmark does not match the other.
B is for Border: The edges are irregular, ragged, notched, or blurred.
C is for Color: The color is not the same all over and may include different shades of brown or black, or sometimes with patches of pink, red, white, or blue.
D is for Diameter: The spot is larger than 6 millimeters across (about ¼ inch – the size of a pencil eraser), although melanomas can sometimes be smaller than this.
E is for Evolving: The mole is changing in size, shape, or color.