Libyan rebels are also building up their forces on the road to Sirte, sending tanks and rocket launchers.
Rebel leaders have appealed to foreign governments to unfreeze Libyan funds.
The UN has already agreed to release $1.5bn (£1bn) in Libyan assets - which had been frozen under sanctions - to help with immediate humanitarian needs.
Closing in In a statement, the MoD said "a formation of Tornado GR4s... fired a salvo of Storm Shadow precision-guided missiles against a large headquarters bunker" in Sirte.
The bunker housed a command and control centre. There is no indication that Col Gaddafi was in Sirte or in the bunker itself at the time of the attack.
"The attack that we launched on the bunker in Sirte last night was to make sure that there was no alternative command and control should the regime try to leave Tripoli."
Nato warplanes also targeted 29 vehicles mounted with weapons near Sirte and bombed surface-to-air missile facilities near Tripoli, the alliance said at a daily briefing in Brussels.
Meanwhile, the rebels are building up their forces around the town of Bin Jawad, preparing for an assault on Sirte, about 100km (60 miles) to the west.
The BBC's Paul Wood, who is with the rebels, says their mood is still buoyant, despite running into unexpectedly stiff resistance.
Rebel commanders think the fighting on the road to Sirte could last another three or four days, our correspondent says.
The rebel administration, the National Transitional Council (NTC), has begun moving to Tripoli, although many senior figures remain in the eastern stronghold of Benghazi.
Speaking in Istanbul, the head of the rebel government, Mahmoud Jibril, said the uprising could fall apart if funds were not forthcoming quickly.
"The biggest destabilising element would be the failure... to deliver the necessary services and pay the salaries of the people who have not been paid for months," he said.
In the Libyan capital, Tripoli, there is continued fighting in the Abu Salim district, one of the last areas loyal to Col Gaddafi.
A Scottish nurse working at the hospital in Abu Salim, Karen Graham, told the BBC they were "overwhelmed" with casualties.
"All the staff were just doing the best we can, but we were literally inundated," she said. "We'd just clear one lot of casualties and the next lot would be getting brought in. Our theatre just couldn't cope... This is the first time we've had such a vast number of people in."
Human rights group Amnesty International says it has evidence that both pro-Gaddafi forces and rebels abused detainees in their care.
Guards loyal to Col Gaddafi raped child detainees at Abu Salim prison, Amnesty said. It also accused rebels of beating prisoners, including a boy conscripted by Gaddafi forces who surrendered to the rebels at Bir Tirfas.
Summary executions The UN is to investigate reports of summary killings and torture through its existing commission of inquiry on Libya.
"We urge all those in positions of authority in Libya, including field commanders, to take active steps to ensure that no crimes, or acts of revenge, are committed," UN spokesman Rupert Colville told Reuters.
The UN has previously said some military action in Libya could amount to war crimes or crimes against humanity.
The BBC's Rupert Wingfield-Hayes visited a hospital in the Mitiga district of Tripoli which had received the bodies of 17 rebel fighters.
Doctors said the group had been prisoners of Gaddafi troops in Tripoli and were tortured and killed as the rebels seized the capital earlier this week.
Dr Hoez Zaitan, a British medic working at the hospital, said about half the bodies had bullet wounds to the back of the head while others had disfiguring injuries to their limbs and hands.
He said the bodies had been examined for possible evidence to be used at a war crimes tribunal.