Vince Cable, the business secretary, is fighting a running battle with the Office for Nation Statistics to block them from continuing to mention a target to cut annual net migration to the tens of thousands by 2015.

Cable wants it to be made clear the target is not government policy, but a goal set by the Conservatives and has nothing to do with the government.

Letters seen by the Guardian show Cable has written to Andrew Dilnot, chair of the UK Statistics Authority, the watchdog that oversees the ONS, to demand that the ONS stop referring to a target in its official publications.

The correspondence, running for months, shows the determination of Cable to distance himself, and the Liberal Democrats, from a target that he regards as wrong, badly constructed and unachievable. It also raises issues over how government statisticians treat targets over which a coalition government has sharp disagreements.

The Conservatives have effectively admitted that they will not meet the net migration target and now refer to it as an aspiration. Net migration into the UK is 260,000 a year and the inability to meet the target has the potential to cause David Cameron a loss of votes mainly to Ukip.

The ONS repeatedly referred to the “government target” between August 2013 and 2014 before downgrading it following Liberal Democrat protests. Since August, it has continued to write in its official publications that “migration statistics are used to monitor the impact of immigration policy, and performance against a stated target to reduce annual net migration to the UK to the tens of thousands by 2015”.

Following Cable’s protests, the ONS statistics director general, Glen Watson, defended the wording, saying in November “referencing a target that users and the media follow closely does not impact on ONS neutrality”.

Watson said: “We concluded that the current wording of the statement provides helpful context for users and I see no sound statistical reason to change it. The net migration target has become part of the media and public discourse; the media and others tend to comment on the net migration statistics in this context. Senior managers within ONS therefore made the decision to leave the sentence as it is.”

Cable escalated the row by writing to Dilnot to say he disagreed strongly with Watson’s decision, adding: ”Whether or not it has become part of the public debate is irrelevant and to continue to state it as a government target does not in any way reflect the coalition agreement.

“The public rightly expects all ONS releases to reflect the facts accurately, given its role as a trusted and respected institution. It is not for the ONS to comment on public discourse or political targets set by political parties and continuing to use this incorrect wording will no doubt compromise its political neutrality and independence thus misleading the public”.

In his initial letter, Cable told Watson: “The coalition agreement states that the coalition commits to introduce a cap on immigration – it does not state the level of the cap the wording you quote is from a Conservative party commitment which my party believes to be unrealistic and unachievable and hence has never agreed to it…It should therefore not be referenced in any official government publication”.

• This article was amended on Monday 2 February 2014. The director general of ONS is Glen Watson, not Graham, as we had it in the original article. This has been corrected.