Mostly yes, and the exceptions are predictable. What matters is what has been added to the paper, not the paper itself.

Uncoated paper and board - plain kraft, un-laminated coated board - is accepted in kerbside paper recycling across the UK. A twisted paper handle goes with it, because it is the same material.
A laminated bag is board with a plastic film over it. Some authorities take it, many do not, and the honest answer is that it depends on where your customer lives.
Specify uncoated kraft or an un-laminated board with paper handles, keep the ink coverage sensible and skip the foil. That bag goes in the paper recycling anywhere in the country with no asterisk.
We will tell you what is on the stock for your job. We do not publish certification claims we cannot evidence.
We price the job in front of us rather than selling a package. Artwork can follow later; the quote does not wait for it.
Not sure which bag? Send a photograph of what you are packing and we will come back with the stock, the handle and a size that fits it.