There is a rumour that someone has been arrested after ticking "No" on one of those Alpha course posters.
This act - like any other graffiti on someone else's property - could well constitute criminal damage: see the relevant Crown Prosecution Service Guidance.
If it is a criminal offence - and so not just a private law infringement - the intention or even the implied consent of the advertiser would not normally matter.
That said, under section 5(2) of the Criminal Damage Act 1971, genuine belief in the consent of the owner of the actual property in question can constitute a defence:
A person charged with an offence to which this section applies shall, whether or not he would be treated for the purposes of this Act as having a lawful excuse apart from this subsection, be treated for those purposes as having a lawful excuse—
(a) if at the time of the act or acts alleged to constitute the offence he believed that the person or persons whom he believed to be entitled to consent to the destruction of or damage to the property in question had so consented, or would have so consented to it if he or they had known of the destruction or damage and its circumstances [...]
It would be interesting to know whether those running the Alpha course could be deemed to have consented, on the assumption that they actually owned the poster in question.
In any case, the CPS would normally only prosecute when it is in the public interest to do so.
It would therefore also be interesting to know whether the CPS would see such a prosecution as being in the public interest.