You're absolutely correct that by convention, applause is discouraged in the House of Commons (and indeed, the Lords). Erskine May, the guide to parliamentary practice, has this to say on the subject:
All Members should maintain silence or should converse only in
undertones. Whenever the conversation is so loud as to make it
difficult to hear the debate, the occupant of the Chair calls the
House to order.
...
The Select Committee on Modernisation of the House of Commons noted in
1998 that, while spontaneous clapping at the end of a speech could not
be interpreted as disturbance of the Member speaking, if the practice
became established it could lead to a situation where the success or
failure of a speech was judged not by its content but by the length of
the applause. Both applause and slow handclapping would ‘disrupt the
tenor of the debate’.The Speaker has indicated that the rule against
clapping did not preclude spontaneous reactions of a non-partisan
character; and that in practice it is a matter of judgement for the
Chair as to whether to intervene where applause has broken out
spontaneously.
The relevant parts of the Select Commmittee's report can be found here.
Some of the more famous examples in which the Speaker has rebuked the offenders include at the debate on the address after the 2015 General Election, which returned a large number of new SNP MPs. These MPs, presumably unaware of the convention on applause, frequently applauded their leader, Angus Robertson, at which then Speaker John Bercow interjected:
Order. May I say at the start of the Parliament that the convention
that we do not clap in this Chamber is very, very long established and
widely respected, and it would be appreciated if Members showed some
respect for that convention? They will get their speaking rights from
this Chair—of that they can be assured. They will be respected, but I
would invite them to show some respect for the traditions of this
Chamber of the House of Commons.
Hansard - 27th May 2015
In another case, current Speaker Sir Lindsay Hoyle jokingly rebuked MPs applauding his election as Speaker.
As to why Bercow chose not to intervene and rebuke the MPs in the specific case you've pointed out, we can only guess. However, in 2016, when asked by Conservative MP Michael Fabricant to give guidance about the current practice, prompted by another instance of unrebuked applause, Bercow gave the following explanation:
I thank the hon. Gentleman for his point of order and his great
courtesy in raising it in the way that he did. The short answer is
that it is the long-established convention of this House that we do
not applaud. For what it is worth, to the best of my recollection, I
have never myself done so. If he is asking me whether I would prefer
it to remain that way, the short answer is that I would. I think that
the convention that we do not applaud but register our approval in
other ways is a valuable one. All I would say to the hon. Gentleman,
who has raised his point in an extremely polite way, is that as far as
the Chair is concerned, each situation has to be judged on its merits.
I am very conscious that I am the servant of the House. If,
spontaneously, a large group of Members bursts into applause,
sometimes the most prudent approach is to let it take its course.
However, I would much prefer it if it did not happen, unless the House
consciously wills a change, and I am not aware that the House as a
whole has done so. In that respect, I sense that the hon. Gentleman
and I, not for the first time and hopefully not for the last, are on
the same side.
Hansard - 3rd May 2016
