I am surprised that your wife didn't need any kind of visa for Switzerland but your wife needs a Schengen visa for Iceland.
You apply at the Danish Embassy in Central London if you want it free if your wife has a BRP. You can pay VFS or TLS but I liked it free and they did it while we waited and Sloane St isn't in the congestion charge zone...
This is the guy I emailed for an appointment for a free visa.
BENTE FEDOROWICZ / BFEDOR@UM.DK
Danish Embassy. 55 Sloane St, Knightsbridge, London SW1X 9SR
Please see No. 5 for required documentation for the application:
Iceland is one of my favourite places but it does knock big holes in the credit cards.