Courts will very, very rarely interfere with a contract but will do if there is concern that the contract is against a public interest or the will of Parliament. Champerty and maintenance fall within that category.
In modern idiom maintenance is the support of litigation by a stranger without just cause. Champerty is an aggravated form of maintenance. The distinguishing feature of champerty is the support of litigation by a stranger in return for a share of the proceeds.
Lord Justice Steyn in Giles v Thompson
Further explanation from the Practical Law Company separates out the differences
A cause of action assigned as a consequence of a transfer of a property (such as a debt) with which the cause of action is closely related, will not offend the rules on maintenance and champerty provided the recipient obtains a genuine commercial interest in the subject of the litigation (Re Oasis Merchandising Services Ltd; Ward v Aitken and others  2 BCLC 493). For examples of what constitutes a genuine commercial interest, see Genuine commercial interest.
An assignment of the proceeds of a claim in which judgment has not yet been given will not offend the rules on maintenance and champerty provided the assignment does not confer any right to interfere in the litigation (Glegg v Bromley  3 KB 474 at page 490, Re Oasis Merchandising Services Ltd; at page 498).
However, an assignment of the bare cause of action so that that proceedings may be brought in the name of the assignee will generally be contrary to public policy (Trendtex Trading v Credit Suisse  AC 679).
The current claims by 3rd party collections company fall into this third group.
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