Not even close, cow’s milk has significantly higher impacts than the plant-based alternatives across all metrics, including processing, transporting, etc.
For instance, it states that producing one litre of dairy milk requires more water than producing one litre of almond milk. OK, and? In itself it means little. Almond farming is creating big water pressure in California, which is already water-stressed. Is having cows in England creating the same water issue? I don't know.
It's not clear what the proportion of transport is in the total emissions. 'Transport' is also vague as it can go from local to intercontinental, as mentioned.
> If you want to reduce the environmental footprint of your diet, switching to plant-based alternatives is a good option.
That strikes me again as avoiding the glaringly obvious option: reduce/stop milk consumption. Otherwise, it sounds like marketing for one product over another one.
https://ourworldindata.org/environmental-impact-milks