Hi Tabby, welcome!
There are only a couple doctors in the UK that we know of on the forums, the most well-known being Dr. Guichet (pretty much by default due to scarcity). There are probably more, but we don't have much information about them.
You can look in the
Limb Lengthening Doctors and
Patient Experience sections and start searching. Specifically you can search for "Guichet" in the latter, we have a few diaries there.
If at all possible, look beyond your home country. Don't limit your selection to proximity, as you want to find the right fit for you. You'll be supporting your body for the rest of your life with your legs, might as well not compromise due to distance. If a local doctor fits your needs I'd just consider it a lucky bonus.
As for the procedure itself, it's not any harder for men or women. Pain tolerance depends on the person. If you want 6 cm, I suggest lengthening your femurs. Internal methods are recommended; most doctors don't even offer external femurs due to severe discomfort that can last over three months. While more expensive, it'll leave smaller and fewer scars as well.
If you suspect that you have shorter tibias proportion-wise, consider externals. It'll be considerably cheaper, but you might not be able to safely lengthen 6 cm so keep that in mind.