Tamsulosin is an alpha-blocker, and there are several other alpha-blockers you could try first, before giving up on them, given they did work.
Finasteride/Dutasteride are 5-alpha-reductase inhibitors - a form of hormone therapy, which is a half-way house to the hormone therapies used for prostate cancer. It prevents the formation of the male sex hormone Dihydrotestosterone (DHT) which is the hormone the prostate and seminal vesicles prefer to use. They create it from Testosterone at point of use using an enzyme 5-alpha-reductase, and it is this process which the 5-alpha-reductase inhibitors prevent, but unlike the full prostate cancer hormone therapies, it doesn't stop the action of Testosterone itself. In the absence of DHT, the prostate and seminal vesicles will use Testosterone instead but it's not as effective and causes them to shrink over a period of about 6 months, often relieving the symptoms of BPH.
DHT is also involved in libido and generating erections, so these might be impacted, but often not to the same extent as with hormone therapies used for prostate cancer. DHT is also used by hair follicles, and its loss may cause a reduction or loss of body hair acquired at puberty (except beard and pubes tend to take years to be impacted), and conversely it may cause a reversal of balding, which is also caused by DHT.
Finally, loss of DHT interferes with PSA production, and hence with your PSA test results, which is important since you're on regular PSA tests. You need to remember to double all your PSA test results while you're on Finasteride/Dutasteride.
I note you mentioned you are being treated at RBH, and that's a centre which does prostate embolisation for BPH. Although this is not used as a treatment for prostate cancer, I have wondered if it might be beneficial for someone with BPH where there's enough concern about prostate cancer to be regularly monitoring for it, as a way to perhaps reduce the risk of prostate cancer with fewer side effects than with conventional treatments. I'm completely guessing here, but that would be a good question to ask them. (It might rule out radiotherapy later, as radiotherapy requires a good blood supply, which prostate embolisation intentionally damages.)