Karzai's term was due to expire on May 20, but Afghanistan's supreme court extended it to August 20 due to the vote being delayed over security and logistical concerns.
Taliban fighters opposed to the government have in recent months been resurgent against Afghan forces and troops from the US and Nato.
Britain and other Nato member countries have pledged 5,000 extra troops for Afghanistan before the election, while the US has promised to send an extra 21,000 troops.
Brown said that while Afghan and foreign forces had provided some security in the southern province of Helmand, there was still more to do.
"If much has been achieved, there is still much more to achieve - especially in the south, the Taliban heartland where British soldiers are fighting alongside brave Afghan soldiers," he said.
"British soldiers ... are striving to defeat the insurgency and bring progress, taking Musa Qala [a district in Helmand] back from the insurgents [and bringing] real progress in the six key population centres there.
"As I sat down with the governor and the local elders this morning, I heard the desire to see Helmand prosper and stabilised, in a future free from extremism."
Thousands of civilians are thought to have been killed amid continued fighting between government forces, US and Nato-led troops, and Taliban fighters.
Aleem Siddique, the United Nations spokesman in Afghanistan, told Al Jazeera: "The reality of the situation is that civilian casualties are being caused - and they are being caused by both sides in this conflict.
"If we look at the last year alone, over 2,000 Afghan civilians perished as a result of the fighting.
"While we have seen measures on the part of the military forces to reduce the level of civilian casualties, we think there is no room for complacency here, particularly as we will see a troop surge taking place in the next few months."