Hays, the UK's largest independent, acquired the two miniples in the space of a week last year, adding 29 shops to its network.
However, the Competition and Markets Authority (CMA) last month issued an initial enforcement order, telling Hays to pause any efforts to further integrate the two businesses.
The CMA said it was concerned Polka Dot and Millington would cease to be distinct from Hays, and that the acquisitions represented a wider competition concern.
Hays Travel has previously said it is committed to cooperating with the CMA throughout a review process, and stressed the two brands will operate separately.
This week, the CMA has invited interested parties to comment on the acquisitions and present any initial views on the impact the two transactions could have on competition in the UK.
Anyone wishing to comment has until Monday 9 February to share their views. The CMA has not yet opened any formal investigations into the two acquisitions.
"This invitation to comment is the first part of the CMA’s information-gathering process," said the CMA. "To assist it with this assessment, the CMA invites comments on the transactions from any interested party. Written representations about any competition issues should be provided by the [9 February] deadline."
Hays's deals for Polka Dot Travel, which had 15 branches, and Millington Travel, which had 14, quickly followed its moves for Spear Travels Group and its 12 shops and Cruise.co.uk parent Victoria Travel Group.
It has also in recent years acquired Hays Travel Independence Group members Travel House, which had 16 shops, and Miles Morgan Travel, which had 19.