Why does my toilet feed service valve still leak?
Thanks for the comments getterdun and bcworkz. 

I went to Toolstation and bought a new service valve and also a new inlet valve for the princely sum of about £11. As per your suggestion I checked the plastic pipe, and it looked a bit rough around the end and one of the teeth of the thread was badly worn, but I couldn't see a way to replace just the pipe so I replaced the whole thing (dismantled the cistern and everything as per a video on YouTube). 

I couldn't get the old service valve off, couldn't get enough grip to turn the valve part opposite to the nut part, so I decided to leave the old one now but give it a really good wipe and test anyway with the new inlet valve and pipe. I also used a fresh fibre washer. At first when I turned the water back on it leaked quite a bit and I was slightly disheartened, but I remembered reading somewhere that fibre washers slowly expand as they get wet, so I just put a bucket under the leak and left it for an hour or so. Bingo! No more leak :)