"His passing is a sad day for us, but every member of the unit is privileged to have known such a likeable, grounded and utterly professional man. We are deeply honoured to have served alongside him."
The spokesman added that the regiment's thoughts and prayers were with his family and friends.
L/Cpl Brown was the fourth British casualty in as many days.
Another British soldier also died on Tuesday. Lance Corporal Christopher Roney, 23, from Sunderland, who served in 3rd Battalion The Rifles, was killed in a fire fight near Sangin.
And on Sunday, Lance Corporal Michael Pritchard, 22, a Kent-born Royal Military Policeman who lived in Eastbourne, East Sussex, died as a result of "small arms fire" - also near Sangin.
The MoD said the Royal Military Police were investigating friendly fire as a possible cause of both of these earlier deaths.
No further information would be released until the conclusion of the inquests, it said.
Most recent UK fatalities
Total deaths 2011: 32
Updated: Dec 18 2011
The BBC's Peter Greste in Afghanistan said the relatively high casualty toll was partly because British forces were aggressively pushing troops out into smaller patrol bases in an attempt to drive the Taliban out.
He said the Taliban had, until recently, been forced back but had since re-grouped, resulting in daily gun battles and casualties.
Our correspondent said the 3rd Battalion The Rifles had had a "particularly rough time", losing eight men since deploying three months ago.
Meanwhile, the funeral of the 100th soldier killed during 2009 while on duty in Afghanistan took place in his home town of Bury St Edmunds in Suffolk on Wednesday.
L/Cpl Adam Drane, 23, of the Royal Anglian Regiment, was shot in Helmand Province on 7 December.
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