Explanatory note #176 on the Gambling Act 2005 specifies:
There are some exceptions to the general prohibition on gambling by children and young people. Children and young persons may participate in all forms of private or non-commercial gaming and betting. Young persons may participate in lotteries and pool betting on association football. Children and young persons may use the category of gaming machine with the lowest stakes and prizes (Category D). They may also take part in equal chance prize gaming at certain premises, as provided under Part 13 of the Act.
Cribbage and Dominoes are both exempt forms of "Equal Chance Gambling" which can be played on alcohol licensed premises (e.g. pubs).
As @richardb points out, while young people (i.e. your son) are normally allowed to take part in Equal Chance Gambling there are explicitly excluded from doing so on alcohol-licensed premises using the "Exempt gaming" provisions as outlined in Sec.280
Children and young people must be excluded from the gaming.
So you can't play for money (assuming the absence of a suitable Family Entertainment Centre license or similar), however playing not-for-stakes doesn't fit the definition of "Gambling" in terms of the act.
Gambling is defined as either "Gaming", "Betting" or a "Lottery"
It's not "gaming" without a prize:
In this Act “gaming” means playing a game of chance for a prize.
It's not "betting" without a prize:
For the purposes of section 9(1) a person makes a bet (despite the fact that he does not deposit a stake in the normal way of betting) if—
(a)he participates in an arrangement in the course of which participants are required to guess any of the matters specified in section 9(1)(a) to (c),
(b)he is required to pay to participate, and
(c)if his guess is accurate, or more accurate than other guesses, he is to—
(i)win a prize, or
(ii)enter a class among whom one or more prizes are to be allocated (whether or not wholly by chance).
And it's not a Lottery either (I won't quote the whole section here as it's a bit wordy but you can check for yourself here)
So as long as there is literally no stakes or prize (whether money or otherwise) you can play with a young person in a pub.