I'm not sure whether your use of a questionmark in the sentence "They said an invoice was sent out on 21st dec, a Saturday?" suggests you don't believe they sent it.
Unless the contract requires them to obtain proof of postage I think that as it's a regular annual bill it will be difficult to challenge it. Also, if the charges are in line with an agreement you signed then it may be difficult to argue against them, unless a legal person advises the terms may be unfair. if the late payment charges aren't in the agreement then you could challenge them.
It may be something to just put down to experience