HMO licence tenants say they are related – Cousins?

I think being related still does not mean that a room that is undersize can be occupied, whether or not it is family home or an HMO,
So from your post it appears that you intend them to occupy each room, but I would say at the time of signing the tenancy two persons were going to occupy the largest room and the third person was going to occupy the next biggest room, irrespective whether they are related or not, it only matters when they are unrelated where you must have an HMO license, just let it as a family house for 3 cousins, ask tenants to prove how they are related, such as common surnames, if not how else are they related, ask them to sign a declaration that they are all related to one another, then I think you are covered, but as for the undersize room, state this clearly on your tenancy agreement that this room is for storage purpose only, and cannot be used for sleeping, if someone finds out they are using it for sleeping then that is not your problem, you cannot tell tenants where to sleep, where to point their beds, when to use loo, when to take a bath, and which room they should sleep in and how many of them should sleep in any particular room, as long as you make it plain that the smaller room can only be used for storage purpose, whether that is wrong or not, that is exactly what i would do and not lose my sleep over it.
At some time in the past someone made that room livable didn't they, its not a new construct is it.

Also be advised that not always surnames can be the same between cousins, as some cousins from maternal side have different surnames.

If you suspect that they are not really cousins then I think it would be too risky. Although you may be able to avoid a Council penalty or fine with the "reasonable excuse" that you made them sign an affidavit or some sworn statement, it wouldn't stop the property being an HMO if they aren't related and if its licensable under a local scheme, you would have to immediately rectify the situation if the Council found out, which may be difficult to do given current eviction times. In addition, it may put you in breach of your insurance conditions as well as possibly lease and mortgage conditions.

if they are from mainland china then they will each have a family card that will show their relationship. you could ask for copies of those.Hukou (Chinese: 户口)

For something like this you need to look at strict definitions. And to claim that the 3 cousins make a single 'household', you need to be able to demonstrate that they are "members of the same family who live together (including couples)."
the .gov.uk website gives guidance as to what comprises a 'family' for HMO purposes, and it examples aunts and uncles, so cousins is obviously a logical extension.
If the whole property is let under a single, jointly liable AST, including the use of the term 'family' when naming the joint tenants, then you would be on fairly safe ground. Ensure that their intention is to share grocery costs, household bills, cook meals jointly and this will add strength to your elbow.
Do make sure however that you don't need 'change of use' planning permission to change the use of the property from HMO to single household as i think this can vary from area to area.
Also, consider any fees that might be chargeable by the Council for a Selective Licence, or re-applying for an HMO licence once these tenants leave.

Cousins are specifically included in the HMO legislation.

Zhorik's suggestion could be useful though.