Actually, you're both wrong. The real significant legal distinction is usually between criminal trespass and burglary (also known as "breaking and entering"), where the latter involves entry with intent to commit some other crime beyond illegal presence. At common law, the "breaking" of the "breaking and entering" element of burglary does not require actual use of force or damage to a physical object.

If I recall right, the "breaking" part can be interpreted as broadly as pushing open a closed (but unlocked) door.

That's the letter of the law, but I sincerely doubt that was the spirit..

In UK law, simply opening an unlocked door and going inside is not a crime. You can come home to me sat on your sofa and all you can do is ask me to leave by the nearest exit (though if I refuse, you can use reasonable force to remove me).