Hi
Have to agree with Snorri. May would certainly be better for daylight and finding afordable accommodation. If you want to ride a lot of hours a day this can be important. If not then maybe it doesn't matter so much.
August is statistically likely to have better weather. But I guess that depends on what conditions you like to ride in. If you like it warm August is more likely to be so, although I agree that you do have to just take what you get - lets face it we've just had the warmest part of the year in October!
There are lots of things to think about other that the time of year to go of course. Blatant self promotion but I have a website designed to help out first time end to enders which helps to guide you through all the things you might need to consider from getting to the start line, nutrition, what to take with you, training, creating your own personalised route and how to trun it into a GPX file and a whole lot more. If you what to check it out (its all free so nothing to lose;¬) ) the site is
www.landsend-to-johnogroats.co.uk.