<p> wouldn't do it unless there was one at the end of every line instead of just at the end of every paragraph. Rename the epub to .zip and extract one of the html files to see what style it is using.
At the beginning of each paragraph it will say something like <p class="calibre4"> . Then look in the .css file to see what it says for that class. Ones that affect line spacing are margin-top, margin-bottom, line-height and padding.