Is there anything I can do legally?
Not a lot really as you're not the tenant in that room. If the landlord/owner is not approachable, one option is to report your concerns using the Tower Hamlets complaints procedures, especially as their website says:
The Council has a proactive inspection programme of HMOs. If conditions in the properties inspected are not up to standard, the landlord or owner is required to improve them.
The legislation on the size for this type of HMO room can be found at para 1A(2)(b) of Schedule 4 of the Housing Act 2004:
1A. (1) Where the HMO is in England, a licence under Part 2 must include the following conditions.
(2) Conditions requiring the licence holder—
[...]
- (b) to ensure that the floor area of any room in the HMO used as sleeping accommodation by two persons aged over 10 years is not less than 10.22 square metres...
Edited to add in response to a comment:
The above quote from the Tower Hamlets website refers to a requirement to "improve" the accommodation which might (or might not) be sufficient to address the apparent breach of licence. However, Section 70 provides the power to revoke licences in certain situations - such as:
(1) The local housing authority may revoke a licence—
[...]
- (b) in any of the cases mentioned in subsection (2) (circumstances relating to licence holder or other person);
[...]
(2) The cases referred to in subsection (1)(b) are as follows—
(a) where the authority consider that the licence holder or any other person has committed a serious breach of a condition of the licence or repeated breaches of such a condition;
(b) where the authority no longer consider that the licence holder is a fit and proper person to be the licence holder; and
(c) where the authority no longer consider that the management of the house is being carried on by persons who are in each case fit and proper persons to be involved in its management.
I do not know if Tower Hamlets would, or would not, use this power in response to a complaint made by a non-connected person but it is an option worth exploring.