See the first link for this description of førerpladsdækning:

"Ved eneuheld, hvor man for eksempel kører ind i et træ, er der ingen ansvarlig modpart. Det betyder, at der ikke er nogen til at betale erstatning i tilfælde af en alvorlig personskade, for man kan nemlig ikke blive erstatningspligtig over for sig selv.
Kun med førerpladsdækning, der tegnes som tilvalg til bilforsikringen, sikrer man sig selv erstatning efter statens takster."

Second link is to examples for "collision coverage", which is what is used in the U.S. to cover this type of loss (as well as damage to the insured vehicle from collisions with other vehicles. The driver's liability for damage to other vehicles and property is under a separate coverage.)

The UK has a different approach, called "comprehensive car insurance cover", explained at http://www.carinsurancebrokers.co.uk/comprehensive-cover.htm... This includes liability cover, unlike the Danish førerpladsdækning and the American collision coverage.

I guess you'd have to specify the lack of equivalence with both the American and British versions.

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Note added at 2 days48 mins (2011-02-03 14:10:35 GMT)
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I overlooked entirely the reference to "personskade" in the Danish, so my answer is wrong. The correct answer is indeed "driver injury cover" as suggested by Mr. Davies.