I lack sympathy, somewhat.
Either you have a contract with that company that they'll pay within a certain time, and you should be working to the maximum of that window. Or threatening them with collection if they don't pay on time as per the contract.
Or you have a contract that doesn't say a word about payment schedules, which means you have almost no fallback without going to a court and proving they were unreasonable (which will cost you more than it's worth).
Though they haven't declared bankruptcy, a "commercial dispute" could easily mean their suppliers have turned off all their IT because they haven't paid, or the bank has shut their account for similar reasons. Just because they haven't declared bankruptcy YET doesn't mean they aren't in serious trouble. Especially if they can't tell you what's happening.
But, this is the risk of self-employment, which is more an opt-out from all kinds of employee and income protections (which still don't save you if you the company goes bankrupt, by the way!). There's a reason you "get paid more" - because you need a reserve of cash, have to fight your own battles, etc. which employed people get paid for them.
Yes, I've been self-employed. For 10+ years. Made a good living out of it, and I gave it up not for any reason relating to not being able to live off it, or being screwed over (I never used an umbrella company, though, but also never had a non-paying client - because a non-paying client isn't a client, they are a debtor). But if a client doesn't pay, you stop working for them and move on. If your umbrella company doesn't pay, you do the same. Pretty much, the excuse does not matter.
In fact, being self-employed, are you not perfectly able to approach your clients direct and ask them to employ you through any other umbrella or even directly? I'm not guaranteeing they'd even consider it, but if you're any good, they'll be glad to hear it surely? And if not, that's the price you pay for freedom of employment like that.
When you choose to opt out of being tied to particular company, client, job, task or obligation that you don't like, this is your price to pay for that flexibility and freedom - though nobody deserves to have their money withheld.
However if you want that freedom and then go back and tie yourself into a company to get the amount of work you need, surely that's the worst of both worlds - absolute reliance on a company that has no obligation to push any work your way? And to not have sufficient reserves to tide you over that is unrelated to self-employment at all - it just means you've not saved for ANY eventuality.