It's not all about battery behaviour. Scotland aside, British Winters aren't cold enough for battery chemistry to be the dominant factor in higher consumption. It's mostly down to higher load. Winter weather offers less mechanical grip and this makes traction inefficient (summer tyres are harder in cooler weather, also reducing grip). Rain and sleet offers greater resistance to forward motion, and winds are higher in Winter which will often present you with headwinds and sidewinds that require more power to keep the car going where you want it. Also, cabin heating is an additional energy demand in winter, and is a significant load. (This is why heat pumps "extend range", they bring waste heat from cooling the batteries into the cabin to avoid needing to produce that heat electrically... sort of like the way petrol engined cars heat the cabin)
All of those factors apply equally to ICE and BEV cars. The reason the BEV figure is more pronounced is down to differences in energy overhead in the power train. ICEs have a large, and fixed overhead: between the various losses at each stage, a petrol ICE uses about half the fuel you put in it just to overcome losses before you even start to deliver useful power. So, to exaggerate slightly, if you put 10 litres in, 5 is basically wasted, and the other 5 gives you your power. But that amount of overhead doesn't increase much with load (how much energy need the engine to produce due to speed conditions etc). This means that an increase in your power demand will show up as a smaller increase in fuel needs: a 20% increase in load means you need "6 litres" of work, but the power train overhead cost still comes to "5 litres worth", so you end up using 11 litres, a 10% increase.
(caveats: the figures aren't exactly that high, the overhead does increase with load, but under normal driving it's not much of an increase)
EVs power trains, by contrast, have very low overhead, so their power consumption pretty much directly follows load: you use 20% more power, the battery drains 20% faster. There's also a cold weather effect of the chemistry, but south of the snow belts, that's only a significant factor if you take lots of short journeys that don't allow the system to warm up (exactly like an ICE in that respect).
You can see the effect of this low overhead even in optimum driving weather with EVs.. if you drive very fast in them, the consumption increases at a higher rate than it would in a petrol car.
