The raids, in which 139 people were arrested on suspicion of immigration offences, attracted widespread media coverage.
They followed criticism of the Home Office for running a mobile billboard campaign telling illegal immigrants to ‘go home or face arrest’.
Fishburn Hedges chairman of public affairs John Williams said the coalition had to be clear it was not stepping into campaigning.
He said: ‘I believe the Home Office has overstepped the mark with its statement, which said 139 "immigration offenders" have been arrested. I believe the correct term would be "suspected immigration offenders", and this reflects some overenthusiasm from the Home Office.’
He added that this sort of publicity was going to be counterproductive on attitudes to minorities and could raise national tensions.
A Home Office spokesman said national and regional media teams were invited to the raids, and a press release was circulated to the media containing a statement from immigration minister Mark Harper.
It said: ‘Today’s operations highlight the routine work we are carrying out every day to stamp out illegal working. We are sending a clear message to employers who choose to use illegal labour: we will find you and you will pay a heavy penalty.’
The Home Office also live-tweeted the event, giving updates on the number of arrests made using the hashtag #immigrationoffenders.
Williams said: ‘What is interesting here is the use of social media to create more impact, because it also creates more heated debate.’