The Daily Mail isn't exactly noted for unbiased accuracy but on this occasion it has provided three separate legal opinions.
Firstly, Mr Justice Ousley has made his decision in the HIgh Court, so it now becomes a legal precedent.
Secondly, the opinion of Findlaw.co.uk (which has the backing of the mighty Reuters organisation, and its teams of lawyers, behind it) is cited.
Thirdly, the opinion of the vastly-experienced Riz Majid, from Neumans LLP, seems to concur with the other two.
So unless the case in the Daily Mail report is allowed to go before the Supreme Court (which I would think would be very unlikely), and the decision is then overturned, it would seem that the act of criminal trespass cannot prevent someone from successfully claiming adverse possession of a property, either now or in the future.