Depends on what you call a "free market". The usual understanding is that a free market relies on the participants having sufficient information and being able to trade freely. However, the necessary information is usually hidden by sellers so that buyers can't make a "rational" decision in what to purchase (see The Market for Lemons: https://en.wikipedia.org/wiki/The_Market_for_Lemons).

Trading freely is compromised as well as markets will almost always favour the larger purchaser and so there's an incentive for companies to become every larger in order to consolidate power and profits.

So, it's not so much that free markets lead to monopolies, but our bastardised version of free markets that lead to monopolies.

Also, free market advocates are rarely advocates of actually free markets, but instead advocates of asymmetric markets that favour the large incumbents.

Of course they lead to monopolies. If you start with a large number of equally capable suppliers and one somehow gains an edge then that one will be more profitable than the rest allowing it to invest and reduce its costs. This makes it even more competitive and provides a positive feedback loop. Eventually its competitors go bankrupt or get bought out by it.

Regulation can certainly exacerbate the problem, for instance rules that have a fixed annual cost or where the costs do not increase in line with volume favour larger concerns.

The idea that a totally free market can exist is a fantasy based on assumptions that simply cannot hold water. Regulation is necessary in order to prevent the powerful from abusing the weak. The fact that there are poor regulations does not invalidate the concept.

I didn't say that free markets lead to monopolies: I qualified that with the need for economies of scale. Those may not exist - but look at most of the markets you interact with in your daily life and try and find the ones that don't.

I'm not aware of how regulation of competitive markets would lead to monopoly. Are you referring to "regulation" in the form of state-endorsed/controlled monopolies? Those usually exist in situations where barriers to entry and economies of scale are so high that the state is simply "getting ahead" of the inevitable monopoly (e.g. national infrastructure).

Of course, corruption could also be what you mean by "regulation" that leads to monopolies, but all of this is predicate on the absence of corruption or cartels. If that's not the case you can throw all your assumption out of the window anyway.

Try playing the Monolopy board game, you'll answer your own question.

Yes, there's an entire body of work, starting with Ayn Rand, that vehemently argues that government interference in the economy is what leads to monopolies.