A series of marches went ahead as part of a global campaign in Leeds, York, Shipley and London throughout the day.
The women are protesting to show support on the same day as the anti-Trump Women's March in Washington DC.
Cat Crossley, co-leader of the Leeds branch of the Women's Equality Party, said more than 1,200 women took part in a march through Shipley earlier today as part of the international protests.
She said ahead of her march: "I'm concerned that having somebody in such a position of power, constantly taking misogynistic, homophobic and racist views is damaging because it normalises those views which are detrimental and anti-progress.
"Donald Trump is going to roll back the years where we have made progress."
The protests in Shipley, organised by the Shipley Feminist Zealots, started in Market Square.
Elsewhere, hundreds of people marched through Leeds city centre from noon in protest against President Trump.
Demonstrators, also joining in with the worldwide campaign, began their march on Briggate, bringing shops, restaurants and much of the city centre to a standstill.
Meanwhile, thousands of protestors descended on central London today for the Women's March, organised to promote women's and human rights.
Organisers announced on stage that 80,000 people had taken part in the event.
Marches have also taken place today in other UK cities including Manchester, Edinburgh, Belfast, Liverpool and Cardiff, with thousands turning out.
About 200,000 people - including celebrities Katy Perry, Scarlett Johansson and Amy Schumer - are expected to take part in a demonstration in Washington DC later on Saturday.
Beginning at the American Embassy in London, the march made its way around the streets of the capital and to a rally in Trafalgar Square.
The movement states on its website that the US election "proved a catalyst for a grassroots movement of women to assert the positive values that the politics of fear denies".
Organisers of the London march called for people to join them "as part of an international day of action in solidarity" on President Trump's first full day in the Oval Office.
People across all ages and genders descended on Grosvenor Square holding a rainbow of placards with slogans such as "dump Trump", "reject hate, reclaim politics" and "no to racism, no to Trump".
Mayor of London Sadiq Khan and his wife Saadiya were in Trafalgar Square while celebrities including ex-England rugby captain Chris Robshaw and Iron Man 3 actress Rebecca Hall were spotted among the throngs of people.
The series of marches and demonstations across the globe come after Mr Trump was officially sworn in as the 45th US President at Capitol Hill in Washington DC yesterday (Friday).
Violent clashes broke out as protestors blocked entrances to the inauguration ceremony before banners and rallies were held in cities across the world.