Just wanted to agree with Joaniepat about GSM, which is the updated term for vaginal atrophy and definitely better and more all-encompassing, as it covers all the areas which can be affected by reduced oestrogen.
I never suffered from actual vaginal dryness, but was prescribed Vagifem to help with the awful watery discharge which so many of us seem to suffer as a symptom. It cleared the discharge up within weeks and has also helped with bladder issues too (in my case, UTI-type symptoms) although this has taken longer. I've read about other women who have found it's helped with leaking. I have no experience with testosterone, but it's interesting to read pp who've said this has been helpful for them. Definitely worth you pursuing the hormonal angle with your GP.
Also re the kegels - the issue can certainly be muscle overtightness, rather than the opposite. I believe that women's physios are available on the NHS, but I just Googled and saw one privately, which wasn't terribly expensive.