Why? This was an administration error. The fact that the decree was acted upon incorrectly doesn't invalidate the decree itself, which says "These two people should get divorced". If the firm needs an additional decree so that they can divorce the right people (e.g. because the original decree has been executed and is no longer valid), then that's what they can ask the judge for.
Otherwise, the victims in this case have the UK tort system available to them to seek a remedy for any damages they may have suffered. They can also just get re-married and ask the firm to cover those associated costs.
England and Wales allow unilateral divorce, and at least the husband wanted to divorce, so even without this mistake the result would be divorce. The mistake must be in the details of the settlement, so there's a good chance it's a material cost that the lawyer who made the mistake or their firm can compensate for monetarily
Financial orders are separate from the granting of the divorce itself in England and Wales and the two can be done in (sort of) either order, confusingly.
It's usually thought of to be in the interest of one (or both) parties not to finalise the divorce until a financial order is made (eg if one party dies in the period between then the other may never get assets they would have done in a financial order; or there may be tax consequences if assets end up with the wrong party for a period). In this instance it seems like this disadvantaged the former wife because she ended up divorced without a financial order in place.
My guess is that a lawsuit would follow and whomever messed up would be on the hook for any losses between what the final divorce settlement was and what it most likely would have been had it been properly negotiated, plus any emotional damages coming from misapplied parenting rights agreements and the like.
Given that they were using online lawyers, likely that is not very much.
If this was in America, depending on the couple's total wealth and circumstances it could run into the several hundred thousand / low millions.
I don't know the laws in the UK or how that would play out there though.