A light-weight bamboo or Merino wool baselayer should keep you dry and relatively fresh in the tropics. Not all synthetic tops react well with mosquito repellent, so natural fibres (not cotton) are definitely best. Cheap options are available online - eBay, natural t-shirt sites, etc.
Light Wicking Layer
Any long-sleeved wicking layer (Merino wool, bamboo or synthetic) will add a light thermal layer and help keep the sun and/or mosquitos off. Travel shirts are good options as the collars help keep the sun off your neck and many are treated with mosquito repellent. Check Sports Direct, TK Maxx, Blacks, etc.
Light Thermal Layer
If you’re venturing above 1,500m in the tropics, a light/mid-weight fleece or heavier Merino wool layer may prove very useful. Simple light-weight fleeces are available very cheaply and Merino wool jumpers can be bought from eBay for next to nothing.
Everyone should own one of these. They weigh as much as a Mars Bar and take up little more room. They can be worn over a baselayer and/or fleece when you just need to keep out the wind or a light shower, meaning they’re great when on the move. We use the Montane Featherlite.
Breathable waterproof jackets do not work nearly as well in warm conditions, but cooler days, altitude or heavy rain may well leave you wishing you’d packed one. As it should spend most of the time in your rucksack, a cheap, packable jacket should work well enough. TK Maxx will probably have something for £30.