The SNP man told the Scottish Parliament it’s “deeply concerning” that for months the threat of redundancy has hung over 40 jobs there.
He said the contrast between the approaches of the Scottish and UK governments to the long running issue has been “stark”.
Mr Hepburn is calling on Westminster to match the Scottish Government’s policy of no compulsory redundancies for jobs like those in the HMRC mailroom.
He said: “During the referendum campaign senior Labour figures, including the MP for this area and their deputy leader in Scotland Anas Sarwar stood outside the Tax Office claiming that jobs were safer there as part of the UK.
“Their silence on this now speaks volumes.”
He said those now under threat were “just the tip of the iceberg, with the Public and Commercial Services union suggesting HMRC will shed thousands of jobs in the coming years.
Holyrood energy, enterprise and tourism minister Fergus Ewing said HMRC had announced in June that two of five regional post rooms would close by the end of this year while the remaining three – including the one in Cumbernauld – will close by March next year.
Adding that those affected face “a very uncertain future” he said more news about HMRC intentions should be forthcoming soon.
Cumbernauld and Kilsyth MSP Jamie Hepburn is pressing the Westminster government to pledge there will be no compulsory redundancies at the mailroom at key local employer HMRC.