So clause 4 goes further than I thought:
http://en.wikipedia.org/wiki/Clause_IVBut there are several positions here:
a) The actual behaviour of the UK Labour in most of the second half of the 20th century. i.e. Essential services nationalised, state players in strategic industries, and private enterprise for the rest. Wanting to nationalise the corner shop would be an extreme position.
b) The stated goals of clause 4.
c) State ownwership of all businesses. To see how this is different from b, I refer you to the abovelinked article.
d) removing "the freedom for individuals to own property" (your phrase). I have lots of property that isn't corporations. I'm sure you do too. People own houses, cars, laptops, clothes, teaspoons, etc.
to conflate b with d as you have done is a cartoonish strawman.