Downing Street said ministers at a cabinet meeting agreed that the use of chemical weapons must not "go unchallenged".
Mr Cable said his party had been willing to back a "properly planned and justified" intervention in Syria, but he warned today that the decision to move ahead without Parliament "fatally undermines the integrity of this mission".
"Bombs won't save lives or bring about peace", the Labour leader said in a withering statement about the strikes, which he labelled "legally questionable".
Mr Corbyn accused the prime minister of "waiting for instructions" from President Trump about what to do.
"The Government should do whatever possible to push Russian Federation and the United States to agree to an independent UN-led investigation of last weekend's horrific chemical weapons attack so that those responsible can be held to account".
President Trump spoke to the prime minister on Thursday evening, and the pair agreed that Syrian President Bashar al-Assad had "established a pattern of risky behaviour in relation to the use of chemical weapons".
"They agreed to keep working closely together on the global response", the statement concluded.
Labour's leader says the PM is not accountable to the "whims of a US President" and asks her to release her "full" legal advice.
Parliament should have been consulted and voted on the matter.
But rival politicians and some Conservative colleagues have called for a parliamentary vote before any British involvement.
Diane Abbott, the shadow home secretary, went further, saying the Labour party believed there was no military answer to the Syrian crisis. In 2013, MPs voted down British military action against the Assad regime and the latest incident raised questions over whether they should be allowed another vote.
"But it is about doing the right thing, it is about actually protecting those innocent people that the Assad regime have so little care for and are quite comfortable in terms of using chemical weapons against them".
The diplomatic discussions are starting to feel like part of a waiting game.
Evidence is still being gathered, but USA officials are understood to have results from blood and urine samples that indicate chlorine and a nerve agent were used in the Syrian town of Douma. Again, we are being threatened.
The prime minister has summoned the cabinet to discuss the government's response to the suspected chemical weapons attack in Syria.
Do MPs need to approve United Kingdom action in Syria?
She told reporters that the president had "a number of options at his disposal and a number remain on the table", but added: "We haven't laid out any specific actions we plan to take".
Amid conflicting tweets about the timing of any retaliation, U.S. president Donald Trump said on Thursday that an attack on Syria could take place "very soon or not so soon at all".
In a subsequent tweet on Thursday, the USA president said an attack on Syria "could be very soon or not so soon at all".
- Demand we stop this war.
The legal argument will form the centrepiece of Mr Corbyn's attack on the Government's handling of the issue when MPs return on Monday after the Easter recess.
Mrs May is still yet to unequivocally point the finger of blame at the Assad government but she has spoken of the need for action "if" the regime is found to bear responsibility.
But he said it was "intellectually bankrupt" to expect the security services to lay out all the information they have.
"Theresa May should have sought parliamentary approval, not trailed after".