Black Watch soldiers were helicoptered into action in the first phase of Operation Panther's Claw.
More than 700 UK troops have launched a major offensive against insurgent strongholds in southern Afghanistan.
The soldiers from the Light Dragoons and 2 Mercian are taking part in the third wave of Operation Panther's Claw, which began two weeks ago in Helmand.
The assault came as some US and Afghan forces met "heavy resistance" from Taliban fighters in the province.
The co-ordinated "surge" of soldiers aims to make the area safe ahead of presidential elections in August.
US Marine Brig Larry Nicholson told the AFP news agency on Friday that his soldiers were in a "hell of a fight" and were facing "difficult challenges" in the southern sector of Helmand province.
Elsewhere in Helmand US commanders say they have met little resistance.
BBC diplomatic correspondent Paul Adams said the object of the US assault was to "take ground and hold ground" - something that had not been attempted before in Helmand.
He said the UK's Operation Panther's Claw, which began a fortnight ago with an air assault on the region of Babaji, north of Lashkar Gah, had broadly the same objectives.
More than 350 troops from the Black Watch were dropped into the area backed by 12 Chinook helicopters in what the Ministry of Defence described as one of the largest air operations in modern times.
Two British soldiers taking part in the operation - Lt Col Rupert Thorneloe, commanding officer of the 1st Battalion Welsh Guards, and Trooper Joshua Hammond, of 2nd Royal Tank Regiment - were killed in an explosion in Helmand on Wednesday.
Lt Col Thorneloe was the highest ranking army officer to be killed in action since the Falklands War.
Thousands of British forces have been fighting the Taliban in Helmand since 2006.
The BBC's Ian Pannell, who is travelling with UK troops in Helmand, says the latest phase of the offensive involves a major land assault, with soldiers backed up by artillery and air support.
Our correspondent said while the British had taken some key towns, their effectiveness had been limited by a lack of resources.
However, the arrival of thousands of US marines had now freed up the Light Dragoons battle group to launch its latest offensive, he added.
The assault has been co-ordinated with the ongoing US operation to the south - named Khanjar, or Strike of the Sword.
About 4,000 marines as well as 650 Afghan troops - supported by Nato planes - have been involved in the surge, launched in the early hours of Thursday.
General Jack Keane - former vice chief of the US Army and the architect of the "surge strategy" in Iraq - told the BBC that the object of the new offensive was to "take momentum" away from the Taliban.
He said: "The first thing we must do is establish security. My concern is - just as we did in Iraq - we will try to go ahead and not truly put in all the resources necessary to get security."
The joint large-scale operation is the first since US President Barack Obama authorised the deployment of 21,000 extra US troops to Afghanistan, as part of a new strategy for winning the conflict.
Many of those troops are being redeployed from operations in Iraq.