I can't advise whether you can have a smart meter with electric storage heaters, which are usually on a separate circuit controlled by a timeswitch. That system always requires the economy seven tariff.
However, I can tell you that off-peak times will vary, according to your location the type of meter / timeswitch and your choice of supplier. (And they are often different. )
If you have an old style mechanical clock, the offpeak period will remian on GMT throughout the year, so the actual switchover will not change, when the clocks go forward to British Summer Time. If you have a physical clock next to the meter, you can check whether the it is showing the correct time. (The clocks are often wrong, which may be in your favour.
But if you have a radio timeswitch, the company that operates the local distribution network broadcasts a radio signal, which controls all of the timeswitches in the area. The switchover times are usually very accurate and everybody with that type of switch will have the same cheap rate period. Similar accurate timings also apply to smart meters.
I have a radio teleswitch, so I replaced the on/off switch for one of my storage heaters with a switch that has a neon indicator. That way, I can always check whether my supply is on the day or night rate (which in my area, runs from 10:30 pm until 12:30 am and again, from 2:30 am until 7:30 am).