Also, if you are CofE your vicar can apply for free tickets on your behalf (only found that out at Westminster Abbey too late). There is a small quota for active parishioners; others may do it too, it's not well publicised.
Other way to access St Paul's (or at least the crypt) is to hold an MBE, OBE or CBE as that's the Chapel of the Order (you and your offspring can marry there as well).
KC is, reportedly, very keen on opening up royal buildings and collections to the public. So I expect we'll seean ever-increasing amount of utter vulgarity, And good on him!