"Go to your cupboard -- I mean, your bedroom. Dudley -- go -- just go."
-- Uncle Vernon (PS3)
A second letter arrives for Harry in the post addressed to ‘Mr. H. Potter, The Smallest Bedroom, 4 Privet Drive.’ Harry, Uncle Vernon, and Dudley wrestle over the letter. Vernon wins the fight and gets rid of the letter (PS3).
This event is dated by the subsequent descriptions of letters arriving and the date of Harry's birthday. We can infer that this letter arrives on a Wednesday because the letter arriving on the day after the next is specifically said to come on a Friday. Counting the days on the calendar back from the 31st, Harry's birthday, places this letter arriving on the 25th of July. In the real world, the 25th of July was a Thursday, so Rowling is off by a day in this passage.
We can determine the time because of the events of the next day. Harry sets his alarm for 6 am and goes downstairs. He encounters Uncle Vernon at the front door who yells at him for "about a half hour," after which Harry is ordered to make a cup of tea. By the time he's done with the tea, the mail has arrived. That would suggest that the mail comes between 6:30 and 7 o'clock in the morning -- which is quite early when you think about it.
For the record, the Royal Mail has tweeted in 2017 that the earliest they start delivery is 7am. https://twitter.com/RoyalMail/status/824246549815431168