yes it is legal. No it doesn't work very well.
Look at the post office website https://www.postoffice.co.uk/branch-finder to become familiar with the red oval logo which you will find on signs indicating a post office, and to find the nearest one near you. Most are not main post offices, they are mostly subs, usually a counter in a shop. If they display the logo they are the real deal.
Post the cards into a proper pillar box - see the article at wikipedia about them for images and a good story, lots of people collect pillar boxes and using them is an iconic British experience - at https://en.wikipedia.org/wiki/Pillar_box
If you leave the cards with somebody they have to do for you what you could have done, and just giving the outgoing mail to a postie delivering mail isn't done - at least not around my neck of the woods - because the delivery office and the sorting office are in different places or at least different departments.
The idea of leaving outgoing mail in the RFD box simply doesn't exist.
Most (all??) British stamps now are self-adhesive - no more licking.
The little metal token indicating the next collection is, unfortunately, also a relic of the past. You'll find an empty slot where it should have been.
Things change, and when privatised they change faster and more.