just so you dont think the others are talking out of their arses, another vote for north to south. When I did Oregon and Cali coast in a June many many moons ago, I clearly recall a few cyclists coming the other way and thinking, "the poor buggers"....
This june trip was also the coolest june I had ever biked in, the coast in general is quite a bit cooler than just a short distance inland--a heads up for you, but being from Blighty you would be accustomed to the weather.


All that said, it is a wonderful trip. There are differing opinions of the northern part, Washington State, a fellow I biked with who had biked through it said he would have avoided it, I started in Northern Oregon so missed that bit.
In any case, there are tons of trip reports and books on this coast trip, so no lack of good info.