Calls to 0300 Numbers are charged at a standard rate (the same as calling a UK landline starting with 01 or 02). Calls to 0300 Numbers are usually included in landline and mobile minutes packages.
Ofcom requires that ALL phone service providers (both landline and mobile) charge exactly the same rate for 03 numbers as they do for numbers starting with 01 or 02. So if (because you've got spare 'included minutes' as part of your landline or mobile package) you don't actually pay anything for calls to normal 'geographic' numbers, calls to 03 numbers are also free. Otherwise you pay the same amount that you would when calling your aunt in London (on an 02 number) or your mate in Sheffield (on an 01 number).
I had to contact the TV licensing people on the 0300 number today, as I received a threatening letter from them, despite using the online option some while ago . I tried three times and the only option that would let me speak to a person was 'bereavement ' ( which was relevant to my query). So I don't think dialling the 0300 number will get you anywhere I'm afraid.