1. If it leaks around the swivel base of the spout only when hot and / or cold are turned on then its the seals for the spout. The two O rings / seals on the brass spigot at the top of your picture. A temporary fix which sometimes works (no guarantees!) is to remove the O rings, wrap a few turns of folded PTFE tape around the spindle where the O rings sit, then refit the O rings.
2. If it leaks when both hot and cold are turned off, it is the cartridge leaking.
3. There are no washers inside, only a plastic cartridge with some O ring seals.
4. To remove the cartridge you will have to:
4a. Remove the chrome ring from around the white plastic lever. This may reveal a large nut holding the body of the cartridge into the tap, or it may be part of the nut.
4b. To remove the chrome ring, check for grub screws under or behind it holding it in place, and remove such screw. Then use a "Boa Constrictor" type rubber wrench to remove ring. Alternatives are rubber gloves, or wrapping tape around to protect chrome then using grips.
5. You will then have to source a new cartridge. Try Showerdoc.
If the taps weren't expensive it may well be better to replace them. Buy a well known make (e.g. Bristan, Crosswater, Vado) and keep the installation leaflet marked up with model of tap. You should then be able to get spares for around 10 years.