A country need only fail on one of the eight criteria to not meet the definition of independent country status. England does not meet all eight criteria; it fails on six of the eight criteria...
1. Has space or territory that has internationally recognized boundaries (boundary disputes are OK).
Yes, England does have internationally recognized boundaries and is 130,395 square kilometers in area. England is the largest component of the United Kingdom of Great Britain and Northern Ireland.
2. Has people who live there on an ongoing basis.
Yes, according to the 2001 census, England's population is 49,138,831.
3. Has economic activity and an organized economy. A country regulates foreign and domestic trade and issues money.
Somewhat. England certainly has economic activity and an organized economy. However, England does not regulate its own foreign or domestic trade, the United Kingdom's parliament acts on the entire nation's behalf.
The Bank of England serves as the central bank for the United Kingdom and does print banknotes for both England and Wales.
4. Has the power of social engineering, such as education.
No. National government departments (such as the Department for Education and Skill) at the national level maintain responsibility for social engineering.
5. Has a transportation system for moving goods and people.
Mostly. England has a transportation system but the system is not fully under English control. There is no English Parliament but some systems are under local control but must of the national transportation system is under national control by Parliament.
6. Has a government that provides public services and police power.
Somewhat. Local governments provides local law enforcement and fire protection but the national government controls criminal and civil law, the prosecution system, the courts, defense and national security across the United Kingdom. England does not and can not have its own army.
7. Has sovereignty. No other State should have power over the country's territory.
No. The Parliament of the United Kingdom definitely has power over England's territory.
8. Has external recognition. A country has been "voted into the club" by other countries.
No. England does not have external recognition nor does England have its own embassies in other independent countries. There's no possible way England could become an independent member of the United Nations.
Thus, as you can plainly see, England (nor Wales, nor Northern Ireland, nor Scotland) is not an independent country; England is an internal division of the United Kingdom of Great Britain and Northern Ireland.