The classic definition of negligence was provided by Alderson B in Blyth v Birmingham Waterworks (1856) 156 ER 1047. Negligence, he said, is the omission to do something which a reasonable man, guided upon those considerations which ordinarily regulate the conduct of human affairs, would do, or doing something which a prudent and reasonable man would not do. The standard demanded is thus not of perfection but of reasonableness. It is an objective standard taking no account of the defendant's incompetence - he may do the best he can and still be found negligent, as in Nettleship v Weston (here).
Cunliffe v Banks  1 All ER 459, Singleton J
A diseased tree belong to D fell across the highway; a motorcyclist P collided with the tree and was killed. The judge found as a fact that D's agent had checked the state of the trees quite regularly, and could not have realised that it was likely to fall. A person is liable for a nuisance, he said, if he causes it, or if by the neglect of some duty he allowed it to arise, or if when it has arisen without his own act or default he omits to remedy it within a reasonable time after he should have been aware of it. But in the instant case D was not liable either in negligence or in nuisance.
Brown v Rolls Royce  1 All ER 577, HL
A worker P regularly got oil on his hands at work, and contracted dermatitis. He alleged that his employers had been negligent in not providing barrier cream (as some other employers did), though they had sought medical advice and did take other measures such as the provision of ample washing facilities. There was no clear evidence to show that the cream would (even probably) have prevented dermatitis, and the House of Lords said the employers had exercised reasonable care.