Yes, they had clocks - the clock at Hampton Court Palace being a wonderful example - http://tudorhistory.org/castles/hcp/clock.jpgMechanical clocks date to about the 14th century in Europe and spring driven clocks would have been around by the Tudor period, but the pendulum clock came along later. I'm going off memory here, but if you need more details, I can recommend some books to you when I get to work tomorrow.
Small watches were also worn during the Tudor period; see Diana Scarsbrick's Jewellery in Britain 1066-1837, pg. 146. There she writes, "Many watches had a bell to sound the hours, and so were calls clocks after the French 'cloche' for a bell..."
In "Wolf Hall" by Hilary Mantel, Thomas Cromwell is unable to sleep and knows it is 3 o'clock and then 6 o'clock. This is 1527. What kind of clock would he have had in his bedroom? Is there any evidence of its existence in his written records?
Spring-driven clocks did exist in this period, true. The first pocket watch, circa 1511, (attributed to Peter Henlein, with some dispute) was spring driven, as were table clocks, but there was another type as well. Look at Holbein's portrait of Sir Thomas More and his family. Hanging on the wall behind them is a weight driven clock. It had no pendulum, having instead a balance wheel device on the top that rotated, side to side. Spring-driven clocks were notoriously unreliable during this time.
Sorry, wanted to add: it's also likely that the Cromwells knew that it was 3 a.m., etc. because of church bells telling the time. They did this 'round the clock, and in 16th century cities, everyone was in earshot of one.
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