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Not sure tea at 5 but those at my office do for a quick drink at 5.30pm

As for reading... that's pretty true. You do see Londoners buried in a book or newspapers on public transport, especially on the Tube. Also, adverts for the latest novels are prevalent in Tube stations as well.

I've been living in London for a year and there is no wide spread tea at 5.  However Brits do drink a lot of tea.

I agree with the above poster though that you will see most Londoners reading all the time on the bus or tube

Reading on bus and tube is inevitable here because of the constant free papers handed out at rush hour -- the gossip rags like The London Paper, London Lite and The Metro.  Seems a bit suspicious that the powers-that-be want us to be reading and constantly distracted with the entertaining but ultimately worthless tripe within these. Dangerous indeed. 
On the tube though,reading is essential because due to the seating arrangements and the London rule that no one speak or look at each other on the tube, these scandal rags are a lifesaver.

I haven't seen a lot of 5pm tea, although the use the word "tea" to refer to dinner in general not only a cup of tea. At work, everybody seems to stop for a tea break at some point in the morning and then again in the afternoon. Oh and they add milk to the tea

They do read a lot, everywhere, in the coffee shops, in the tube, in the tram, in the bus, in the train, and there are bookshops in almost all stations!