My living complex has free poop bag dispensers by the poop clean up stations (just a trashcan and the bags, basically). I think the cost is probably included in the fees I pay to use my neighborhood amenities (pool, gym, trash collection, etc). However, they're not always good about refilling the bags when they run out, so I buy my own from the store. Plus, it's not like my dog always poops near the station, so it's nice to always have my own handy.
I live in America, and I don't know of anywhere else to get free poop bags. Many people just use the plastic bags you get from the grocery store as a free alternative. You can also get them pretty cheap at a dollar store, but I personally find that those break easily and are too thin for my tastes.
I usually buy in bulk to reduce costs. I spend about 14$, which is about 8 or 9£, for 16 rolls (240 bags). That much lasts me a good number of months. I consider the purchase just another one of the many costs of owning a dog.
If I was paying a tax that included free poop bags like you are, I would go for it and get them for free. No point paying the tax and then not taking advantage of the service you payed for. Even though I pay for mine, I would give a stranger one if I saw them in a predicament (like if my neighborhood dispensers were out).
Anyway, I don't see an advantage to non-biodegradable bags. All they do is prevent the poop from naturally composting once it's in a landfill somewhere. Some people feel they are thicker than degradable ones, but I don't notice much of a difference, personally.