Need help figuring out where/how to pull apart tap please

This type of tap is quite common, and you were right to stop before forcing it, as damage usually happens when too much pressure is applied. Many taps without a visible grub screw have the handle either threaded onto the spindle or covered by a thin decorative shroud that unscrews rather than pulls off. Try gently twisting the handle anti-clockwise instead of pulling upward, using a cloth or rubber grip to avoid scratching. Sometimes mineral buildup causes it to seize, so lightly warming the handle with a hair dryer can help loosen it. Once removed, there is usually a retaining nut underneath that gives access to the O-rings or cartridge. If the leak is coming from the base of the tap, it’s often a body O-ring, which may require loosening the tap from under the sink. If the sink starts flexing, it’s best to stop, as older handles can crack and be difficult to replace. Hope this help you.

Thanks for the replies, much appreciated. I have been trying to lever off the hot/cold indicator with zero success. It has only scratched the surface and it really does seem like it won't come off. I'll keep trying though because I agree it seems like this must be it, surely. Nearly every youtube video shows the same thing too.