I'm engaged in a 'purple ink' war of letters with our council over pot holes after I suffered god knows how many punctures and split a back wheel.
At first they just stonewalled me saying they did what they legally had to do blah, blah, but eventually paid for most of a new set of wheels.
They are currently saying they'll only repair holes that are 40mm deep – it doesn't matter if a hole is in a really dangerous position for cyclists and is 35mm deep, although if you report one they'll usually seem to fix it just in case you have an accident and try to sue them.
This site has some useful information:
http://www.potholes.co.uk