There is only one way to manage the ever changing english weather and that is layering (and being prepared for rain at any and all times). England is all well and good during winter when the weather remains fairly stable throughout the day, only changing really a few degrees day to night. Then, you pretty much know what you're doing and dressing for the day is (in general) not a problem.
Here's a problem I have found though. Whilst throughout the day the temperature may remain fairly stable, first thing in the morning is cold and the evenings, with us drawing ever nearer to Autumn, are also much cooler. So, thats a basic outline of weather (which I'm sure you were all really enjoying reading). Another issue comes around when you're commuting, if you use the morning train, its air conditioned and thus you will end up cold. If you use tubes (undergrounds), you will soon realise that they're really hot. Its great when you're coming from your morning train and are more or less frozen solid but about 5 minutes in, it quickly becomes an issue.
So, here's where I come in. My suggestions are as follows:
If the weather says that there will be no rain: DO NOT BELIEVE IT
England is famous for rain and it almost certainly will and always when you least expect it. I recommend keeping an umbrella with you at all times and one in absolutely every single place you can think of. This means making sure that there is always one in the handbag you're using, one at your desk, one in your car (if you have one) etc...
If the weather is around 20 degrees and partly cloudy:
Think light layers. If you're wearing jeans or pants, you want those with a pair of shoes of your choosing, basically whatever works and doesn't totally kill you when you're busy walking the streets of London. Then add a T-shirt and on top of that a jersey. Easy to take on and off in the case of cold trains or hot tubes also light enough to pop in a bag should you need to do so. If you want to wear a dress or skirt, the basic principle is the same, light dress or skirt and t-shirt (can be sleeveless) and then a jersey on top of that (can be in the form of a pull-on jumper or a cardigan). Easy peasy.
If the day seems a bit colder, you can add a light blazer or jacket on top of that. As it gets colder, a coat with no lining should do for Autumn progressing to a trench coat for colder Autumn days and winter. The t-shirt can change from short sleeved to long sleeved depending on the weather.
And that is the easiest way to layer.
Also, a quick note: If you have a favourite pair of pants but they're too light for Autumn/Winter or even a colder day, get some leggings and layer up that way. You can also still show off ankle and shoes and the bonus with leggings is that you get no stocking hugging from your pants!