Grew up in the southern US and just spent a couple weeks in the Philippines:

• cold drinks
• fans
• lightweight, breathable clothing

That's about it - the sweat is unavoidable

I live in Chihuahua, Mexico, where it usually means dry heat so pretty much anything works but it also means you can use a thing called swamp coolers that pretty much just increase humidity by humidifying air and shooting it quickly. They are incredibly efficient.

Sad part is when it gets humid (in monsoon times) it really doesn't sufice, so an AC is required or just remove as much clothing as possible.

Clothing does help a lot with dry heat, you can use thin fast-drying clothing and that helps evaporate sweat which takes away most heat. Again in humid heat you really can't cool unless you dehumidify with an AC (which is incredibly efficient the more humid the area is, and can be inverted to be used as heaters for much cheaper than gas or normal resistive electric heaters).

In the UK I think your best bet is a reversible heat pump.

Time also helps. The longer and more you spend in the heat, the more you get used to it. Your body will adapt.

I come from the cold north and live in a tropical area now. The heat used to kill me. It still does 15y later, but I can handle it much better than before.

Run cool water over your forearms.

If you have a bucket of ice water you can dunk your arms in for extra effect.

Helps cool you down pretty quick.