20mg Tamoxifen tablets are generic and dirt cheap. Never heard of anyone being refused in last 4 years (except on medical grounds, typically if you're at risk of cardio issues or DVT), but most often you do need to ask for it.
The other tablet sizes are massively more expensive.
I was prescribed 20mg/day, but told to start with twice a week and adjust to symptoms. It's quite slow acting.
It is liver toxic for some people, and my liver wasn't happy with more that about 40mg/week. It is worth getting a liver function test done when you've been on it for 3-4 months.