In a word, no. You don't pay us a bean for using our service or any of its features. You simply pay your phone provider the cost of your call to the 03 dial-in number. The same goes for the other callers on your conference.
And what's so great about that?
Well, if you're a UK caller and have bundled minutes available at the time of the conference, the call will be included in these minutes, otherwise it will be charged by your provider (not by WHYPAY?) at your standard landline rate (the same rate you get charged for calling 01 or 02 numbers).
Feeling sceptical? Take a look at this page from Ofcom, which explains the charges for calling a UK 03 number.
Please check your provider's information regarding the details of your bundled minutes package, as some providers start charging after a certain call duration (usually 1 hour). However many providers allow you to hang up and re-dial before you reach that point in order to avoid being charged, since they then see it as two separate calls.