The report also criticised the government's interpretation of a 1989 EU embargo on arms sales to China, saying the UK should have taken a stricter line.
In particular, the report singles out a "disturbing degree of muddle and confusion" in the operation of licences to Zimbabwe after August 1998 when that country intervened in the Democratic Republic of Congo.
Foreign Office Minister Peter Hain said the government would look at ways of improving accountability, but added that this administration had been more open about arms sales than any previous one.
Prior scrutiny
The Quadripartite Committee - comprising members of the defence, foreign affairs, international development and trade and industry select committees - is demanding the same powers of prior scrutiny afforded to their counterparts in the US and Sweden.
"We are convinced that accountability demands that Parliament is engaged in scrutiny of arms export licences before as well as after their grant.
"Prior scrutiny should be designed to ensure that Parliament has a voice in matters of such crucial importance before final decisions are taken," MPs said.
But Foreign Office Minister Peter Hain told BBC Radio that only last week the government had published an annual report detailing where exports had been granted, and insisted the government's openess was exemplary.
"We are more open, more accountable, more transparent, as indeed the committee of MPs readily conceded, than any other government has been, probably than any other government in the world.
But he indicated that the government would consider implementing the committee's recommendations if there was a way of ensuring commercial confidentiality.
Arms to Zimbabwe
The report said granting licences allowing the export of spare parts for Hawk aircraft to Zimbabwe this February, although later revoked, had "undermined the force" of an EU resolution criticising the regime of President Robert Mugabe.
MPs pointed out the UK had co-sponsored the EU resolution and its behaviour "seems to have constituted a breach of the UK's national criteria".
The report also criticised the government's interpretation of a 1989 EU embargo on arms sales to China, saying the UK should have taken a stricter line.
It also said it was "dismayed" the government had taken five months to respond to its previous report on strategic arms exports published in February this year.
Immediate powers
The MPs have asked for the new powers to be in place "forthwith," from the next session of Parliament.
Liberal Democrat Spokesman Menzies Campbell supported the committee's demand.
"The kind of major embarrassment which the Conservatives suffered over arms to Iraq and the minor embarrassment which this government suffered in relation to arms to Indonesia can easily be avoided by scrutiny, by allowing the searchlight of parliamentary accountability to get into the innermost nooks and crannies of arms export policy," he said.
Shadow Foreign Secretary Francis Maude said the committee's criticism of licences for Zimbabwe was a "good epitaph" for the government's ethical foreign policy.
"Many were appalled when Labour granted licences for Hawk jet spare parts to Zimbabwe despite evidence showing that those planes were being used in the violent and bloody military adventure in the Congo," he said.
"This latest report will consign Labour's 'ethical' foreign policy to the growing scrap heap of their broken promises," he said.