London , England ( CNN ) -- A crowd of students marched through central London on Wednesday , disrupting traffic and shouting slogans in a protest against an increase in university tuition . Students also protested in other cities across Britain , including Leeds , Cambridge and Birmingham . Police said there had been 15 arrests in London and one each in Oxford and Glasgow , Scotland . Three of the arrests happened after students filled Whitehall , the street that runs from Trafalgar Square past the prime minister 's residence toward Parliament . Police penned the protesters in at either end to try to limit criminal damage , and a line of police in fluorescent yellow vests kept the students from reaching Parliament Square . `` We 're kettled , we 're freezing , everyone needs the toilet , but we 're having fun , '' protester Clare Solomon told CNN , using a local term for being penned in . Solomon , the president of the University of London student union , said police had been containing them for five hours as of 6 p.m. ( 1 p.m . ET ) . `` Obviously , people are starting to get angry now . Everyone is really hungry , '' she said . But she thought the demonstration was a success . She estimated 20,000 to 25,000 people had turned out . Police said they could not give an estimate of the size of the London crowd . `` Students are starting to self-organize , '' Solomon said . `` If we can get 25,000 on the streets with no major organization , it 's a sign of things to come . '' British universities should not follow the American model , where students have to pay large tuition fees and seek loans or grants themselves if they ca n't pay , she argued . That excludes poor people from higher education , she said . Students held signs saying `` Stop Education Cuts , '' `` Education not Segregation '' and `` Unite and Fight . '' They managed to break into a police van inside the containment area in Whitehall after smashing the windshield , spray-painting the sides and trying to topple it . Other students stood in their way and tried to stop them . Some students set off firecrackers in the crowd . Otherwise , unrest did not appear to reach the level seen during similar protests two weeks ago , when protesters invaded the building holding the headquarters of the Conservative Party . The students are angry about government plans to allow universities to charge as much as 9,000 pounds ( about $ 14,200 ) a year in tuition fees , a substantial rise from the current cap of 3,000 pounds ( about $ 4,700 ) . The government wants to raise the fees and scrap some subsidies for university students as it tries to cut a massive budget deficit . Defenders of the plan say universities will not necessarily charge the maximum they 're allowed to , but education experts have disputed that . In the protests two weeks ago , students spray-painted anarchy symbols , broke windows and set off flares at the Conservative headquarters before being forced out . Some set fires and shot off firecrackers outside the building . That violence marred what was otherwise a largely peaceful protest . The National Union of Students said 50,000 demonstrators were on the streets in that protest . Two officers were injured in the London activities , London 's Metropolitan Police said . A female officer broke her hand and a male officer suffered leg injuries , police said . CNN 's Richard Allen Greene and Jo Shelley contributed to this report .
NEW : Police pen student demonstrators in for hours , a protester says . Students are angry about government plans to allow tuition increases . Score: 6 Other protests are reported in Leeds , Cambridge and Birmingham .