I very much doubt that a fee is payable for a visit - remember the family members of an EU Citizen can come to live in the UK without paying for a visa on an EEA Family Permit so it would be strange if there was a fee for a visit.
However, my take on the content in that link is that it hinges on proof that the person is a genuine family member of an EU Citizen and it seems that the form of proof required is a residence card. The web page does however go on to state (in Arriving at the border without a visa) that the traveller should be allowed to prove by any means that they are the family member of an EU Citizen and if they do, they should be allowed entry.
You'd be well advised to find out exactly what her immigration status in Denmark is and also pay attention to the section that states you should contact the embassy of the country you wish to visit (in this case not you, your MIL) to find out what documents are required. I'd think the easiest route is for you to call the UKBA and ask.