British paratroopers are moving in large numbers into the centre of Basra's old city in an effort to flush out possible Iraqi fighters.
British armour in Basra on Monday
Three soldiers were killed in an overnight assault as troops reportedly took control of most of the city.
Defence Secretary Geoff Hoon said the UK troops in Basra had achieved a "tremendous amount" and were "there to stay".
Meanwhile, Iraq's southern commander Ali Hassan al-Majid - known as Chemical Ali - has reportedly been killed during an air raid in Basra on Saturday. The reports have not been officially confirmed.
A large contingent of the Para's 3rd Battalion has moved on foot into Basra's old city - a network of narrow passageways and streets.
Military spokesmen have said they believe remnants of Iraqi forces may be hiding there.
BBC correspondent Ben Brown, travelling with 3 Para, says that "minimal" resistance has been encountered so far.
British army sources say 300 Iraqi combatants died during the Basra operation, though it is not clear how many were regular soldiers, and how many "irregular" militia members.
Earlier on Monday, a presidential palace in the city was seized by Royal Marines 3 Commando with little resistance, said the BBC's David Bowden.
Most of Basra is now under British control, a military spokesman added.
Mr Hoon said he was "enormously proud" of the British troops in Basra.
"They have moved into the heart of the city. They are now in Basra to stay. They have done a fantastic job." he said.
Air Marshal Brian Burridge, commander of UK forces, told a media briefing: "The people of Basra are getting their first real glimpse of the courage, tenacity and professionalism of our armed forces."
West: Black Watch, Scots Dragoon Guards and Irish Guards
Centre: 2nd Royal Tank Regiment
North and Docks: Royal Regiment of Fusiliers
South and Palace Area: 3 Commando Brigade Royal Marines
Old Town (on foot): 3 Battalion of Parachute Regiment
He said the operation would change from a military one into a "peace support" mission.
Iraqi commander Ali Hassan al-Majid - who is Saddam Hussein's cousin - is reported to have been killed in an air raid on Basra two nights ago.
He ordered a poison gas attack which killed thousands of Kurds in 1988.
The BBC's Hilary Andersson said that if he was confirmed dead, it might leave resistance in Basra "incoherent".
She said that there was a "sense of relief" among many Iraqi citizens living in Basra that military action might be drawing to a close.
She said: "Many people have been traumatised by what they have been going through."
One of the British casualties to die in Basra was named as Fusilier Kelan John Turrington, 18, of the Royal Regiment of Fusiliers.
The other two fatalities will not be named until their families are informed.
The bodies of 10 Britons who have died in the war will be
brought home on Tuesday and repatriated at
RAF Brize Norton in Oxfordshire. Thirty have died in total.
Group Captain Al Lockwood, British forces spokesman, said the narrow streets of the old city made it difficult to enter using tanks.
But he said that residents were helping by pointing out where militants were hiding.
He said: "There's just this one area we need to clear out and then Basra will be liberated."
He said that the British advance into Basra had been met with "jubilation" from Iraqi civilians.
Colonel Chris Vernon, said British forces have pushed to the Shatt-al-Arab - the city's main waterway.
Some civilians were happy to see the troops entering the city
He said it could take up to four days for troops to gain "strict control" of Basra.
Major General Peter Wall, Britain's deputy commander in the Gulf, said he was cautious about how much control they actually had in the city.
Troops could go "anywhere in a tank", he said. "Of
course, that's not by any means the level of security we're