How do I fix a leak in this toilet cistern inlet pipe?
That looks like standard UK 15mm copper pipe with an olive and compression fitting.



The correct term for the "washer" is an "olive". It is made from copper. If it is damaged, you will have to 


buy new "15mm compression olives", they often come in a pack of 5.
cut off the old olive (you can get olive splitters to do this job)
clean up the end of the pipe with wire wool (or similar) until bright and shiny.
make sure the end is circular and undistorted for at least 1 cm
make sure there is no burr or lip at the very end (use fine grit sandpaper)
slide a new olive over the pipe (above the compression nut)
ensure the parts to be connected are clean
screw everything together 


So long as everything is clean, smooth and undistorted, you don't need any plumber's gunk, gloop or PTFE tape.

Don't overtighten, if it weeps you can tighten a 16th of a turn or so.

If necessary, you can cut the pipe further down and fit an extra joint with a short length of new pipe, you might be able to use a flexible connection hose for future convenience - some of these can incorporate an isolation valve. A professional plumber would use an end-feed soldered copper joint but you can get ring-solder joints that just need heating with a blow-torch. Compression joints are easy and compact (and my preference) but you can also use push-fit connectors (HEP2O, Speedfit, etc) so long as they say they are OK for copper as well as plastic pipe.