Discrepancy with Economy 10 times?

This sounds really strange. When you say you’re seeing this on your ‘smart meter’, it rather sounds as if you’re looking at the In-House Display (IHD). The meter itself is fixed to the wall somewhere out of the way, in a cupboard or in a box on the outside wall. Meters don’t usually show ‘rates’ in pence. I’d ask you please to change the display on the IHD to show ‘Using now’ or similar in kW. 

It’s probably chilly enough these days (your timings indicate that you’re in Scotland north of a line from Dumbarton to Dundee) for you to have a storage heater switched on. If it’s controlled by the meter, it should be very obvious when a heater comes on, because IHDs usually have ‘traffic lights’ that show orange or red when a large current is detected. A storage heater will show a ‘using now’ figure of 1.5-3.5 kW. When that happens, check both the time (to the minute) and the current ‘tariff per kWh’ - it should be the offpeak rate. 

The randomized offset Blastoise mentioned will not be more than 30 minutes, and in most cases is 15 minutes or less. It’s not strictly ‘random’ because it’s fixed for your meter, but it’s just different from every other meter’s. Your afternoon offpeak slot should start between 2.30 and 3.00 pm. It’s probably more difficult to see when it ends, because storage heaters and immersion heaters won’t always charge up for the full extent of the offpeak period. If you see the ‘using now’ figure suddenly go down, it’s not necessarily because the offpeak slot has ended; it could just mean that a heater has reached capacity and been switched off by its thermostat. If you spot this happening, check the ‘tariff per kWh’ again. It should stay at the offpeak figure until sometime between 5.30 and 6.00 pm, with the delay beyond 5.30 being the same as you observed at the start of the period.

If this doesn’t explain the timings you’re seeing, perhaps you could tell us exactly what you observed.