Shulchan Aruch Yoreh De'ah 400:2 rules that a mourner observes the private mourning practices of shiv'ah on shabbat. This includes not engaging in marital relations, not washing in warm water and not studying (most parts of) Torah.
Rema to Shulchan Aruch Orach Chaim 554:19 notes a custom to refrain from marital relations on 9 Av which falls on shabbat. Mishnah Berurah 554:39 explains that this custom holds that private mourning practices apply on Shabbat 9 Av, and thus washing hands in warm water would also be forbidden.
However, with regards to Torah study on this shabbat, Mishnah Berurah 553:9 prohibits only after midday.
Why does Mishnah Berurah allow Torah study before midday on Shabbat 9 Av, but forbids marital relations and washing?
A hint towards one possible answer:
Magen Avraham 553:7 provides a justification for such a practice by positing that Shabbat 9 Av has the status of erev tish'ah b'av, but that marital relations are prohibited due to stringency.
In order to use this Magen Avraham to explain Mishnah Berurah's position, one would need to explain why marital relations and washing would be more deserving of stringency than Torah study.