I am non-EU nationality, but married to Italian nationality, and I have Permesso di Soggiorno mentioned (MOTIVI FAMILIARI)
Is it allow me to enter UK with my wife as per subject 10,20 of law? or need for travel permit?
Travel Stack Exchange is a question and answer site for road warriors and seasoned travelers. It only takes a minute to sign up.Sign up to join this community
You can enter the UK without a visa or family permit, with your wife, if your card says "carta di soggiorno di familiare di un cittadino dell'Unione." In that case it is an article 10 card. It could also indicate permanent residence, in which case it's an article 20 card, but I don't know the exact wording in Italian. It will certainly end with "di familiare di un cittadino dell'Unione."
If your card doesn't say one of those things, then you'll need a visa or, of your trip falls before the end of the transition period, an EEA family permit.
If your card truly says permesso do soggiorno rather than carta di soggiorno then it is probably not an article 10 or 20 card.
(This of course assumes that you do not hold a nationality that entitles you to enter the UK without a visa in your own right. If you are, for example, a citizen of Canada, then you don't need a visa in any case.)