7-17 April i'm going to England
York, Bath, startford upon Avon, Windermere, Edinburg , London
Is coat necessary ? what can we expect the weather in April? How can I prepare my clothes ?
It won't be freezing, but it will be changeable, possibly windy, and will probably rain at some point - of the places you mention, my money is on Windermere for the highest likelihood of rain. The Lake District is famous for it. Edinburgh (which is in Scotland, not England!) is likely to be cooler than further south. Especially in April, you really can get four seasons in one day in the UK. April temperatures can range between 5 and 25 degrees - but they're most likely to be in the mid-teens, with a mixture of sunshine and showers and a few cloudy days, too.
As for clothing, the magic word is LAYERS. When you head out for a day's sightseeing, you need to be prepared for all weathers. As a base layer, wear jeans and a T-shirt in case it gets warm and sunny. Then wear a warm sweater on top, for the days when it will inevitably cloud over and get a bit chillier. You'll definitely need a waterproof rain coat of some kind - one of those with a detachable fleecy lining is ideal. You can wear the coat with the lining on colder days, and on the sunnier days you can just stuff the outer waterproof layer in your bag in case of sudden showers. Some kind of headgear would be useful too, to protect you from wind or sun. As for footwear, trainers/sneakers are ideal for April - it's too cool for sandals but too warm for boots.