The problem is that it is difficult to prove, either way. Unless the envelope in which it arrived is postmarked, you cannot prove they sent it, deliberately or otherwise, late. Likewise, unless they have a proof of posting certificate, they cannot prove they did send it on the date they say.
You would need whoever delivers your post or someone at the local sorting office to sign a witness statement saying that it was only delivered on the date you say it was.
Whatever you do, you are now waiting for a claim to arrive. If/when it does, come back for further advice on how to deal with it.
