The Postal Services Act 2000 is clear that an offence is created if anyone intentionally delays the post or intentionally opens a mail bag. The Act goes on to say: "A person commits an offence if, intending to act to a person's detriment and without reasonable excuse, he opens a postal packet which he knows or reasonably suspects has been incorrectly delivered to him."
Which, as even non-lawyers will easily appreciate, is not the same thing as throwing away a letter because you can't be bothered to deliver it yourself. It could be argued, though, that putting mail in the bin counts as a "delay", albeit an indefinite one.
But the chances of being able to complain to the police about a negligent neighbour throwing away your letters is pretty slim, simply because of the difficulty of finding out about something you probably did not even know was on its way to you.
And even if there was evidence that someone had opened your letters, proving that they had done so intending to act to your detriment would be no easy task.
Incredibly rare
A Royal Mail spokesman admits it's unlikely prosecutions could be brought, simply because of the difficulty of getting evidence. Furthermore, he's not aware of anyone having been prosecuted for throwing misdelivered mail away.
The reported cases of prosecutions for tampering with the mail are incredibly rare, and involve rogue postmen.
http://news.bbc.co.uk.../magazine/3687109.stm