Not any more, they don't!

[Derek Jempson]

This clipping is from the Hastings & St. Leonards Observer dated 21st July 1937. As can be seen, it was proposed by the local Royal Mail to both collect and deliver mail on a bank holiday. Not so nowadays! I wonder which bank holiday the announcement refers to? There isn't one around this time of year in the present. I think I'm right in saying that in those days, there were three mail deliveries each day - early morning, mid-day and late afternoon. Now, we get just one daily delivery, which can be at any time between about nine in the morning and four in the afternoon.

[Insomniac]

I believe they only do box collections on Bank Holidays now, I've never signed up to do it myself, so not sure if it's every BH or just random one's they've selected...
If you find yourself getting your mail closer to 4pm, it's more than likely your postie is on overtime or simply struggling to get around within their time, which is even more common these days with the company trying to save money and cut more hours to please the current and potential shareholders.
It wouldn't surprise me if a few years down the line us Postmen are working closer to your standard 9-5 hours with larger deliveries which have absorbed the deliveries cut out of your local office to cut even more hours.