EWI is the gold standard. It doesn’t make the house “cooler” or “warmer” what it does is prevent the external temperature affecting your wall temperatures so rapidly, keeping the inside more constant.
so solid brick walls have a u-value of around 3 IIRC, but if you put 120mm EWI properly fitted with no air movement inside the insulation etc you reduce it to less than 1 (I think something like 0.7 or 0.8).
u values are a measure of how fast a material transmits heat. The basic principle is that energy (heat) moves to entropy (cold) until the two equalise. There are other factors (air leaks etc) but u value is what EWI affects. The lower the value, the slower the transmission of energy. If you do not have EWI and it’s 40 degrees outside, you have that heat baking into the walls which absorb that energy and start transmitting it inside the house. Aside from uvalue, materials also have something called thermal mass, which refers to how much energy they can absorb. So essentially when it’s really hot, your walls heat up. they don’t heat up immediately because as the heat is being transferred it’s also warming up the walls. This is why even at night in the UK (when it’s very cool even in summer) the house is unbearably warm because the walls are still giving off residual heat from the day.
So EWI takes advantage of both of these factors- if you have a way of regulating the internal temperature, EWI will allow you to compete with the external temperature by making the thermal transfer from inside to outside very slow.
Internal wall insulation on the other hand isn’t as good- you can’t take advantage of the thermal mass of the walls to help regulate the temperature. You can however slow down the thermal transfer. Additionally I wouldn’t be putting 120mm of insulation inside my house because it would ruin my internal space. So the improvements will neither be as good or as efficacious. But as ever, it’s a balancing act.
coupling EWI with a properly insulating ceiling/loft, and then properly sealed floors from air leaks, your house will be substantially more stable. The problem is UK houses are designed to breathe through their air leaks, so just make sure you open windows for 10 minutes every few hours to allow the air to exchange.