The population increase of magpies is because the legislation that used to allow free shooting of them is no longer in force.
Now there are strict controls on who can cull Magpies.
Has the legal position on corvid control changed recently? I remember farmers shooting rooks when I was a child and they still do and use Larsen traps today, never has been illegal on your own land.
The well documented increase in Magpie population from 1965-1990 is often blamed for songbird decline though there is no proven link. Cats take many more songbirds than magpies, woodpeckers are skilled nest thieves should we shoot them too? songbird food and nest sites have declined due to changing farming practices. The BTO are the scientific body looking at bird population here is some of their info on magpie.
http://www.bto.org/birdtrends2005/wcrmagpi.htm
Interestingly once the population leveled out in 1990 clutch size decreased from average 6 eggs to 4. This is exactly the sort of natural balance that most creatures well up the food chain exhibit. Foxes also adjust their breeding rates significantly depending on mortality. So what I am saying is that by going out and shooting a few you are not going to significantly alter the population, they will simply up their breeding and move back in from surrounding areas. It is rare that predation whether by natural predator or man is the limiting factor on a species population. The forestry commission have spent an awful lot of money experimenting with gray squirrel control, they have found that all trialed control methods had zero effect on population size 1 year later. They now target their control to create a dip in the population just at the time that they strip bark from trees but accept that population size is governed by other factors, particularly habitat, food supply etc.
Seems to me we simply don't like anything that is successful whether it be rats, magpies, gray squirrel or Canada goose. The same is the case in woodlands, we dislike sycamore so much simply because it is successful. It will reach a balance in our woodlands eventually, it is not invasive in Europe. I remember reading old forest management records from the 1930's on a property where I worked and they were cutting elms out because they thought they were invasive. Nature will have its way, magpies. rats and sycamore will reach their own balanced population and folk shooting or felling them will not alter their numbers. It may make you feel better, especially when you have been watching a songbird nest for a couple of weeks and then see it robbed. Nature can appear cruel, we lead very insulated lives..