Some 5000 demonstrators marched to Parliament Square where a small group broke away and breached temporary barriers to confront police outside the Houses of Parliament.
"Various missiles were thrown at the officers," Scotland Yard said in a statement. Three officers suffered minor injuries. By mid-afternoon there had been no arrests, it added.
The breakaway group later attacked a nearby Starbucks coffee shop and threw chairs from another restaurant at police, witnesses said.
Wednesday's march (local time) was the first mass protest by students in the British capital for three years.
Four protests against Prime Minister David Cameron's austerity measures shortly after he came to power in 2010 led to clashes with police, assaults on public buildings including the headquarters of Cameron's Conservative Party, and almost 400 arrests.
Students are angry at Cameron's government decision to hike tuition fees and they have been joined by other campaigners unhappy with spending cuts.
"Today we are marching through London in what is likely to be the biggest demonstration in several years," the National Campaign Against Fees and Cuts said on its website. "We could well be on the verge of a new wave of student activism."
It addition to Wednesday's march, students were also planning walkouts and occupations of campus buildings.
