About one in ten colleges are closed but the government says most are open or partially open.
On Monday the court rejected the government's bid to stop the National Union of Teachers' action on the grounds that it is political.
NUT members held a rally and march in central London.
They then marched to the Department for Education where they handed in a letter for Education Secretary Nicky Morgan.
The government had argued that the action was unlawful because it was not in furtherance of a trade dispute as it was not predominantly about terms and conditions of employment.
But the judge had refused to grant the government an urgent declaration that the strike was unlawful, saying the likely outcome of any trial of the issue was that the NUT's strategy was to protect members' terms and conditions through its campaign.
NUT deputy general secretary Kevin Courtney has called the decision by Mr Justice Kerr a "victory for democracy and common sense".
The union says government cuts to sixth-form college funding are having a direct impact on members' terms and conditions while risking colleges' financial viability.
David Igoe, chief executive of the Sixth Form Colleges Association, described the impact of the action as "pretty tame" with only a handful of England's 93 sixth form colleges closed - though many had seen classes cancelled.
He told the BBC there were about 3,000 NUT members in sixth forms out of a total teaching staff of about 8,000.
The association says the NUT action is counter-productive, although it agrees colleges are underfunded.
The government says it is disappointed by the strike. It says 16 to 19 core funding is now protected and the unfair difference between school sixth forms and colleges has been ended.
In last month's ballot, 86% of National of Union of Teachers members in England's sixth-form colleges voted in favour of strike action on a 44% turnout.
Members were asked: "In order to persuade the Secretary of State for Education to increase presently inadequate funding levels which cause detrimental changes to terms and conditions within the sixth-form college sector, are you prepared to take a day's strike action?"
In the vote, 1,453 were for the strike and 235 against, with one spoiled paper.
Thousands of teachers in sixth-form colleges in England are staging a one-day strike over funding cuts after the High Court ruled the action was lawful.