All staff at one branch have resigned, TTG understands, with colleagues at a further two stores also leaving. The three branches affected are Blaby, Nuneaton and Syston.
It is understood some of those who decided to leave did so over differences of opinion about how operations would continue under Hays Travel.
Guy Fletcher, Millington Travel's sales and marketing director, moved to reassure TTG it was business as usual for Millington Travel.
"I can confirm all Millington Travel shops are trading, and we are delighted new managers and team members have joined the business," he said. "These new staff members have joined us with vast industry experience and will add new dynamics to our successful team."
It comes as the Competition and Markets Authority (CMA) seeks industry views on Hays Travel's acquisitions last autumn of Millington Travel and fellow miniple Polka Dot Travel.
In December, the CMA issued an initial enforcement order, telling Hays to pause any efforts to further integrate the two businesses.
The CMA said it was concerned Millington and Polka Dot 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.
In January, the CMA 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.
Hays's acquisition of Millington brought a further 14 stores under its ownership, and Polka Dot another 15. They followed Hays's acquisitions of several other miniples in recent years, including Miles Morgan Travel, Travel House and Spear Travels.
Following a request for comment from TTG, Hays Travel reiterated it is cooperating with the CMA and is unable to comment while the review is under way.
The CMA said it did not comment on ongoing investigations when approached by TTG.
