I work in Windermere and at the moment we're all walking around in t-shirts, its still rather warm and humid! In 4 weeks time it still could be lovely weather, sometimes our Autumn weather is better than the summer!
you definitely don't need a ski jacket, but don't forget your waterproof jacket (we carry these around with us 365 days of the year!) and if you're planning on doing any walking, bring waterproof trousers too.
Otherwise just normal clothes (i.e. t-shirt and jumper, with a warm coat/jacket if needed) will be fine. Umbrellas are pretty useless here since it's often too windy.

