While both are correct (-ish), your first option is unclear and may often be misinterpreted.
You are using Merriam-Webster's first definition:
1: in proximity to : near
However, definition 3b can also be used in a valid interpretation of the sentence:
3b: not later than
// be there by 2 p.m.
Using this definition, the sentence would mean that consumption reaches its peak at any time before the end of the day - which evaluates to any time during the day. While this results in a fairly meaningless sentence, and thus many people will be able to determine what you intended to convey, it is also the more common definition in the context of timeframes, and will cause unnecessary confusion.
Therefore, the second option is more clear. It is, however, slightly incorrect - it should be written:
Overall, the highest number in terms of consumption of energy is in winter and its peak is at the end of the day in England.
It also reads somewhat strangely; I might suggest altering it to something like:
Overall, energy consumption in England is greatest in winter, with daily consumption reaching its peak at 10:00 pm.
Note that this assumes "in England" refers to the location (which is unclear in the original). If it instead refers to the time zone, that would preferably be specified.
Additionally, "end of the day" is potentially vague, especially in winter - it may refer to the end of daylight hours or midnight. I recommend using a specific time if possible.