She was aged 10 in 1996 when her father, Rinat Ibragimov, took up the post of principal double bass with the London Symphony Orchestra, and the family moved to England.

In the following year, Ibragimova began her studies at the Yehudi Menuhin School (where her mother was professor of violin) under Natasha Boyarskaya.

In December 1998, Ibragimova performed with Nicola Benedetti at the opening ceremony of the 50th Anniversary of the Universal Declaration of Human Rights at UNESCO in Paris; they played Bach's double violin concerto under the baton of Yehudi Menuhin.

After winning several international competitions, in 2002 Ibragimova won the London Symphony Orchestra Music Scholarship (formerly the Shell Prize), an important early boost to her career.

The next breakthrough came in 2005 when Ibragimova played and directed Mozart's second violin concerto with the Kremerata Baltica in Mozartwoche at the Salzburg Mozarteum.