For one, the Popular Knowledge picture of the 'peasant mob with pointy sticks' is definitely Not A Thing. On the other hand, depending on how you define 'peasant', 'levy', and 'peasant levy', we might come up with a "maybe?".

So here's a few posts from my Medieval Armies Compilation that all deal with what I think we can agree look reasonably close enough to peasant levies. Starting from a personal favourite, a trio of posts from u/Goiyon:

• This is a general overview on the composition and raising of an army;
• and this is a closer look at the levy system;
• and if you really want detail, a much deeper examination of the levy of the Netherlands;
• u/BRIStoneman has two posts on the pre-Norman Conquest fyrd and how they worked;
• and u/Hergrim looks at peasant recruitment in 1100 AD England.