You've obviously been watching another programme, then Woofgang.
What they do is not 'proving' anything. The value of the estate is known; what is unknown is if there are any heirs. no heirs are found, the estate goes to the Crown, so reduces out tax bill (ha, ha). Of course they won't disclose the identity or any other details about the estate that they have identified, which are invariably intestate.
So they are on for a 'finder's fee'. Their costs are irrelevant to the OP; all that matters is signing a contract at minimum % that means they disclose what they have discovered, in exchange of a percentage of the proceeds. And of course, no money upfront.