Having already lost its technical majority through the disaffection of backbencher Sir John Gorst - who is continuing his non-cooperation protest against the closure of the casualty department of a local hospital - the Government's strength in the House was reduced to 322 by Mr Mills' death, against 323 for the combined opposition parties.
While the formal move into minority will have no immediate impact, it adds to the Government's difficulties and it will further sap Conservative morale.
Tory MPs are already facing a Labour war of attrition in the Commons through the withdrawal of "pairing" arrangements, which means that they have to remain on standby for an opposition ambush. The Government's frustration was illustrated by a series of votes on the Crime (Sentences) Bill on Wednesday night, when a handful of Liberal Democrats forced more than 200 Conservative MPs to remain in the Commons - even though Labour Chief Whip Donald Dewar had told his MPs that they would not be required to stay.
But the real problems could come on the committee stages of legislation such as the Finance Bill, which implements the Budget. As The Independent reported yesterday, no agreement has been reached between the Government and Opposition about the composition of the Finance Bill Committee, for which the Opposition is arguing that there should now be no government majority.
If that question cannot be resolved by next week, then there might have to be a vote of the whole House - and Mr Mills's death could mean defeat for the Government.
Balanced legislative committees mean the Government could not carry its own amendments because in the event of a tie the chair, by convention, casts its vote for the status quo.
But Number 10 appeared determined to soldier on, and the record of the last Labour government showed there is no reason why that should not continue. The 1974-79 Labour government suffered 42 Commons defeats before it was ousted by one-vote on a motion of no-confidence in March 1979.
Although there were few details available on the death of Mr Mills, whose body was discovered yesterday at his London flat, government whips had been concerned that he was one of four MPs missing from Tuesday's vote on the second reading of the Finance Bill. One government source said he had been missing without permission.He was described by one source as "a heart attack waiting to happen".
The 56-year-old MP had a 14,699 vote majority in Meriden at the 1992 general election, and had represented the constituency since 1979. A by- election will be overtaken by the general election, even if that does not take place until 1 May.
t Labour has a lead of 18 points over the Conservatives, according to a Gallup poll published today. The survey for the Daily Telegraph shows Labour on 50.5 points, the Tories on 32.5 and the Liberal Democrats on 10.5.Reuse content