I'll ask the question here, ignoring any debate around the pro's/con's of face coverings, would making them mandatory in enclosed spaces (shops, offices, even schools) not have a benefit in trying to balance the economic and health issues we are facing?
I work in a 100% masked environment and that coupled with social distancing has meant we have stayed productive during the lockdown (how productive will be indicated by the number of smiley boxes you've acquired at home).
The confidence, be it false or otherwise that wearing a mask brings has to have a positive impact and for a lot of people it might actually give them enough confidence to become an active part of the high street economy.
We have to learn to live with and around this virus and so I'd say that for a government that likes to use psychometric and behavioural data, face coverings would be beneficial from that standpoint and depending on which research you choose to believe, it won't be particularly detrimental from a health standpoint in the grand scheme of things.
If you want to see what raw-dogging reopening looks like then the horror show across the pond might persuade you to get behind the wearing of face coverings as one small part of getting back to something like normal.