What you need to take with you as essential items when walking and hiking depends a bit on where it is your are planning to go - you are unlikely to require a torch and survival bag when strolling around the shores of Buttermere.
However, if you are planning to go further afield, you need to consider what might happen if you or a member of your party sprains or breaks an ankle - or the weather suddenly changes when you are high on an exposed ridge.
Good weather and warm temperatures in the valleys can offer a false sense of security - the temperature and wind levels are often very different after only a few hundred metres of ascent.
Here is a list of what is commonly considered the absolute minimum when hiking in the mountain and fells.
Food & Water for the day - see Hill Skills > What to Take - Nutrition
A little Extra High Energy Food for emergencies.
Suitable Clothing for the environment - fleece, hat, gloves, waterproofs, sunglasses - see Hill Skills > What to Wear - Clothing
Some Spare Dry Clothes (eg extra fleece) for emergencies.
Suitable Footwear - see Hill Skills > What to Wear - Footwear
Detailed Route Plan - either one you have devised yourself in advance by studying the map or by purchasing one from a professional and reputable source like go4awalk.com.
Compass & Knowledge of how to use it - see Hill Skills > Navigation.
Basic First Aid Kit - see Hill Skills > Emergencies > First Aid.
Pen/Pencil and Paper
Watch (or means of telling the time)
String (surprisingly useful for all sorts of things)
Swiss Army Knife (just as useful)
A Survival Bag
These last two items may be your only means of summoning help so make sure you always have them with you. See Hill Skills > Emergencies > Contacting the Emergency Service.
Ice Axe & knowledge of how to use it (essential in snow and ice) if walking in Winter
Crampons - just as essential in snow and ice if walking in Winter
A suitable Rucksack or Day Sack to carry it all in.
A Rucksack or Day Sack Liner will keep all your items dry should the weather turn. (There are commercial rucksack liners available but a bin liner is perfectly adequate - just don't forget to check it every couple of weeks for holes/deterioration).
Even together, the items above weigh very little.
But if this all seems a bit excessive, remember:
Better to have and not want - than to want and not have.