Would anyone know what is this toilet chain peice is called?

FLUIDMASTER DUAL-FLUSH REPLACEMENT BUTTON CHROME (edited)

Is this what you want - amazon.co.uk/Twy…AQI

Screwfix sell a complete flush assembly, but it appears to include the bit that you've broken. screwfix.com/p/f…173

Chain? what part has a chain?

Its a dual flush push button for a cable operated flush valve...as @001Cisco and @Killer have said it looks like a Fluidmaster make but its hard to tell. Personally I dont know if they are interchangeable between makes. Theres a few makes out there Fluidmaster / Thomas Dudley/ Siamp/etc

Why dont you just lift the toilet lid off and follow the cable back down to the flush valve and look for a make on it?

Its easier just to change the button mechanism that to change the whole valve.

The Fluidmaster push button shown in the links has a chrome spacer on it so you can either use as shown in the pics or just have a shallow button

Thanks everyone appreciate it