I now of course realise I could and should have done it all myself. I think I'll just have to pay up, again!
You could have done it yourself, but it's done and you're still quids in, so don't beat yourself up about it.
Definitely DO NOT pay them, though - if the FB page had, say, 5 companies on it, they could all be after £300 (plus VAT) each out of your £1,000 windfall!!!
Think of it like asking several builders for a quote to build an extension - you only actually pay the one you choose and appoint to do the work.
To re-iterate, they may say that you signed an agreement to pay them a percentage of all monies that they claim on your behalf, in which case tell them that you will indeed pay them a percentage of any EXTRA money that they successfully claim for you - bearing in mind that the deadline for claims already expired over three months ago....
If they persist in threatening you and demanding payment, tell them to document and prove what work they did in order to 'win' the claim that you'd already received a settlement for and paid the company that assisted you in it.
You might even find that both 'companies' are just brands of the one same company and they're either trying it on with you, now that their golden goose has been killed, or are just woefully incompetent.
YOU DO NOT OWE THEM ANYTHING - DON'T PAY THEM A PENNY!!!!