Insect/Disease on Shtubs
Based on your photos we are not able to identify the shrub. You can send us additional photos of the whole shrub, around the base, and the foliage so we can see what you are dealing with.
The white spots looks like white prunicola scale, a sucking insect. This insect is often found on cherry laurel. Here is more about it http://extension.umd.edu/hgic/plants/armored-hard-scale-trees-and-shrubs
Here is some information on control. Prune out any dead or dying branches. You can scrub off the white scales with a soft brush.
You will have to check for crawlers starting in May (there may be three generations and they are salmon colored) before you spray. Wrap some of the branches with double-sided sticky tape to monitor for crawlers. When you see the crawlers, spray with a summer rate of horticultural oil. Follow all label directions. Do not spray when temperatures are in the high '80s in hot weather.