The CD, titled Never Mind the Dovecotes, features the tracks 'Anarchy in the UK' and 'Pretty Vacant' from the Pistols' sole studio album Never Mind The B*llocks.
In response, Sex Pistols frontman Lydon said: "I would like to be able to trust the National Trust but from this point forward I can't. I was very proud to collaborate with The National Trust back in 2003 and voice a radio advert for them.
"No-one however has even spoken to myself or my management or had a conversation with myself or my management about this album. Never Mind The.... Permission."
He added: "Thievery as I have always thought seems to come from very high places. Whatever happened to the art of conversation?
"As of yet, I am still not sure what the game is in all this. I love my England, my honest England. My heart is true, but this particular situation seems deeply sneaky and we are waiting to be supplied with information on this chain of events, and the answer better be good."
The National Trust compilation also features fellow punk bands GBH, Siouxsie and the Banshees and X-Ray Spex, whose frontwoman Poly Styrene died earlier this year.
> John Lydon: 'PiL lyrics got burnt in house fire'
Watch the Sex Pistols play 'Anarchy in the UK' live on So It Goes in 1976 below: