Ministers were warned of a "serious risk" the military would not have all the equipment it needed to invade Iraq, the inquiry into the war has heard.
Air Chief Marshal Sir Jock Stirrup, the head of the armed forces, said defence chiefs "simply didn't have enough time" to source everything they wanted.
It would have made a "significant difference" if the military had been given six months, rather than four.
A shortage of body armour was blamed for one of the first UK deaths in Iraq.
Questioned about the issue on Friday, former Prime Minister Tony Blair said the military had assured him that troops were ready for the mission.
Sir Jock, who was the deputy chief of defence staff in charge of equipment at the time of the invasion, in March 2003, singled out problems with supplying enough body armour, desert combats and boots for frontline troops.
He said: "The problem of course was that we simply didn't have enough time, as it turned out, to do everything we needed to do before the operation started."
Asked whether having an extra two months to prepare for the war would have helped, he said: "I think it would have made a significant difference. That's 50% additional time.
"We were finding that in a number of cases we were getting 100% delivery about a month or two after the operation started. So I think that the six-month assumption wasn't a bad one."
The inquiry has already heard evidence that planning for the war was affected by concerns that public military preparations could damage diplomatic negotiations.
Sir Jock insisted defence chiefs had voiced their concerns to politicians about the tight time scale.
He said: "We made it absolutely clear to ministers that if we were not allowed to engage with industry - and that was the critical element - we could take these no further and that there was a serious risk that they would not all be delivered by the assumed start of operations."
There had been problems with equipment shortages on the ground being communicated back to London, he said.
Sir Jock told the inquiry: "The other area where we could have done better is in terms of enhanced combat body armour. We didn't have enough of that in theatre at the time.
"And I think, in part for both clothing and body armour, the issue was it was all done so rapidly at the last minute. No-one was quite sure who had what.
"For example, just before the start of operations, the clear message that we were receiving in the Ministry of Defence was that all unit demands for enhanced combat body armour had been met.
"But quite clearly not everybody who needed it in theatre got it."
The shortage of body armour was blamed for the death of one of the first British soldiers killed in Iraq.
Tank commander Sergeant Steven Roberts, 33, who was born in Cornwall and lived in Shipley, West Yorkshire, was shot dead by a comrade while struggling with an attacking Iraqi near the southern city of Al Zubayr on March 24, 2003.
The 2006 inquest into his death heard he was left exposed by "serious failings" in the Army's supply and training methods which meant he had had to give up his body armour just three days earlier.
Sir Jock's predecessor, Gen Lord Walker, told the Iraq inquiry that the funding situation became so tense in 2004 that there was a danger of chiefs resigning en masse.
He said: "There was indeed a list of stuff that we were having to make decisions about and I think we drew a line somewhere halfway down the page and said, 'If you go any further than that you will probably have to look for a new set of chiefs'."
This never happened, but Lord Walker said: "It makes it sound as though we were happy with what was above the line. We weren't happy with any of it."
During his appearance before the inquiry, Mr Blair said he had never turned down a request for equipment from the military while at No 10 Downing Street.
"If anyone had come to me and said it is not safe to do this because of the lack of proper military preparation, I would have taken that very seriously," he said. "But they didn't and they got on with it."
Lord Boyce, head of the armed forces at the time of the invasion, has said he was prevented from discussing issues of logistics and resources in autumn 2002 because it would send out the "wrong signals" as the UK tried to get support for UN action against Iraq.
But despite the rushed preparation, he said he was "confident" frontline troops were properly equipped when they entered Iraq.
Former International Development Secretary Clare Short will give evidence to the inquiry on Tuesday.