You can get plenty wet in 20 minutes. I'd recommend getting a fully waterproof jacket more like
http://www.chainreactioncycles.com/M...?ModelID=17968 and over trousers like
http://www.wiggle.co.uk/altura-night...-overtrousers/ and possibly overshoes.
I also wear cycling tops as cotton compromises the breathability of the jacket. Makes for an easy change to get out of the sweat and wet and let it hang to dry. I get away with toweling off and washing my top once a week.
Obviously get a skullcap if you wear a helmet to keep your head from freezing in the wet. There are many of the market with different weights. I finally got one last winter that had extra material over the forehead and ears to keep those sensitive areas from freezing cold.
It does cost a small fortune, I know. But with the right gear you can ride in any amount of wet thrown at you in comfort and go from fair-weather cyclist to all-year commuter.