Before the war even started, Britain began to evacuate civilians from the major cities. 3.5 million people (especially women and children) were moved to the countryside or overseas, to protect them from bombing raids.

About half the school aged children in London were evacuated. There were further waves of evacuation when the London blitz started and when there was perceived to be a danger of German invasion on the south coast.

Besides evacuation, air raid sirens gave warning of enemy bombing raids so that civilians could get to air raid shelters. Some 177,000 people slept in London Underground stations at night during the height of the blitz to remain safe from bombs.

Civilians volunteered as wardens who enforced the blackout so that German bombers would have more problems identifying targets and as Fire Watchers, patrolling the streets and roof tops during raids to spot and extinguish incendiary bombs before they could start deadly fires. The Boy Scouts were organized as the "Blitz Scouts" to guide the fire department through the bomb rubble to get to fires and fight them before they spread.

Every anti aircraft gun in Britain was deployed in London parks, along with search lights to try to illuminate the attacking bombers and shoot them down. Barrage balloons flew over London, so that their tethering wires would cut off the wings of enemy bombers which flew too low, either to pick out targets or to try to escape AA fire or British fighters. The RAF Fighter Command equipped night fighters to intercept the bombers and shoot them down.

Early in the blitz, the Defenses worked fairly well by day, forcing the Germans to turn to night raids. British defences started out very inadequate against night attacks. They got better quickly, however, more radar sets, directing AA guns and installed in better night fighters gradually improved the defence. By November 1940, London's defences had become tough enough that the Luftwaffe shifted strategy and began to concentrate on other British cities.

By May1941, British night fighters were intercepting the incoming bombers over the English channel and having increasing success in shooting them down. The Blitz was over. The Luftwaffe had attacked Britain's cities and civilian population in 16 cities for 8 months. They lost over 500 bombers.

40,000 - 43,000 civilians were killed across Britain in the blitz. Another circa 130,000 were wounded or injured. This was a far lower casualty count than the British had estimated prior to the war.

In 1937, the Committee for Imperial Defence estimate that a 60 day bombing campaign might cause 600,000 deaths and 1.2m wounded among the British Civilian population. These estimates had seemed to be validated by the bombing experiences in the Spanish Civil War, such as the bombing of Barcelona. In actuality, civilian casualties were less than 10% of these estimates.

So, in answer to the question, quite a lot was done to protect the British civilians from bombing raids in WW2, and what was done was quite effective. Evacuation, air raid shelters, active damage control, and strong defences which first drove the enemy out of the daylit sky and into the night, and second made the night too dangerous for the German raiders to stand the losses all protected civilians to a much greater extent than pre-war estimates had feared.

Sources;

http://www.bbc.co.uk/history/events/germany_bombs_london

http://en.wikipedia.org/wiki/The_Blitz

http://en.wikipedia.org/wiki/Evacuations_of_civilians_in_Britain_during_World_War_II

They did not have the technological capacity to drop their bombs precisely on the target area. Because losses were enormous, they did not fly on low altitudes. The RAF stopped daytime bombing, so the inaccuracy even increased. The USAF did bomb in daytime from very high altitudes.

Where the USAF had a doctrine of targeting industrial capacities, the RAF had not. The RAF bombed civilian targets indiscriminately. Since the USAF did not have the technology to precisely bomb their industrial targets, it made no difference for the civilians on the ground.

The only way for the USAF to hit the target was to use carpet bombing tactics. It meant that whole stretches of cities were destroyed including civilian neighbourhoods. And not only German civilians were suffering: also the occupied Allied friendly nations were bombed heavily. And rightly so to the dismay of the governments in exile.