Well it's only very serious in law if you think that an offence only triable by magistrates and punishable with a maximum of six months imprisonment and a fine is very serious ! But it can be very serious, in context, to the individual.
[ Postal Services Act 2000 s 84(3) ]
The offence under s 84(3) is where a person intending to act to a person's detriment and without lawful excuse opens a postal packet which he knows or reasonably suspects to be incorrectly delivered to him.
That would cover this case., methinks He's at the address and has taken a letter as though it were to him. . The subsection is worded to cover a whole range of possibilities.
The first step is to report it to the police explaining what has happened, how you know, and, above all why it's important to you and what reason the landlord would have for opening the letter. What does he hope to discover? What benefit would that be to him and what detriment, harm , could it bring to you ? (Note that the section refers to intending detriment)
The police ,at the very least, should warn him of the possible consequences of such action so he doesn't do it again. What further steps they take will depend on advice they get from the Crown Prosecution Service.