How do I replace the cartridge on this tap?
Unfortunately that seems to be a discount "unbranded" faucet; in other words it is likely mass produced in the far east or is an unlabeled version from a more common manufacturer. As such, finding parts diagrams to help with disassembly will probably be just as difficult as finding any actual parts.

I will say that the cartridge for this style is commonly accessed by removing the chrome "button" at the top of the handle, then removing a screw underneath that holds the handle on. Once the handle is unfastened and removed (which may require a handle puller tool if it's stuck), then the threaded chrome collar is unscrewed anti-clockwise (when looking from the top). Then the cartridge can be pulled directly out.