Are there any requests from the floor?

With a flying rabbit, a new role for the bell of the tuba, audience voting and wall-to-wall surprise, the Budapest Festival Orchestra's late-night Prom tonight promises to be unlike any the Royal Albert Hall audience has experienced. The BFO and its founder and chief conductor, Ivá* Fischer, will follow their normal concert of Mahler and Liszt with an extraordinary event in which the music will be chosen on the spot, by the audience.

It is a concept that may boggle the imagination of many concert-goers, but in Hungary the BFO has made it a popular feature of its concert series. Fischer suggests that the practice fulfils a purpose beyond simply keeping listeners on their toes.

"The idea came when I witnessed a first rehearsal of a theatre company with actors around a table reading through a play," he says. "It was fascinating because everybody focused on the story, on 'what comes next', without any thoughts of interpretation. I also read about historical occasions, like Schubert's Great C Major Symphony being played through by the orchestra of Vienna and then abandoned, considered unplayable. So I thought that the polished, well-rehearsed product isn't the only musical experience. It is exciting to take part in a first rehearsal, when we simply read through a musical work."

In practice, the event carries implications well beyond that of a glorified rehearsal. Apart from being huge fun, the concert's requirement that everyone take part in choosing the music seems to give every audience member a sense of involvement quite different from merely booking a ticket. Effectively, this is musical democracy in the making.

It may sound zany but there is a daring and originality to the concept, as well as a sense of risk that could shake up audience and performers alike. Fischer says: "In a normal concert one expects perfection and one is interested in the interpretation. Here we will be happy if we manage to play a work through without major disaster and interpretation is out of the question. There will be a very welcome purity and simplicity in these readings."

Here's how it works. On the way in, everyone attending will be given a list of around 300 pieces. Fischer will introduce the concert from the podium, asking everyone to look at the list and decide on a work, in case they are the lucky person selected to pick one.

Next, seat numbers are stowed in the bell of the tuba and three members of the audience are requested, at random, to go on stage and draw out the lucky winners. The people in those seats then get to choose a piece each.

At the Proms, matters are further complicated. The promenaders, obviously, do not have seats, so now it is time for the flying rabbit. Fischer, we hear, will toss a toy bunny into the arena. The person who catches it will get to make a choice.

Are regular favourites likely to pitch up? Maybe, says Fischer, but maybe not. "In my experience half of the people choose the most well-known works, like Ravel's Bolero," he says. "The other half have personal favourites ranging from Haydn to Bartók."

Now the entire audience votes on which one of the several chosen works the orchestra will play – the piece attracting the biggest show of hands wins. While the BFO's librarian dashes off to find the correct orchestral parts, members of the orchestra will entertain us with Hungarian folk and Gypsy pieces. Then, finally, the chosen piece will materialise... depending on the length of the works chosen, all this will happen several times.

It sounds almost impossibly elaborate, especially for an orchestra on tour, but the BFO is no ordinary orchestra. It is an international favourite, not just for its high standards but for the irrepressible spirit with which it approaches music-making. Fischer's nomination for this year's Gramophone Artist of the Year award is the latest in a string of accolades that have recognised him as one of our best-loved conductors; he infuses performance with ideals that reach parts other maestros and orchestras usually do not.

Fischer founded the BFO in 1983 with those ideals in mind. The orchestra declares simply that it "belongs to the music lovers in Budapest and all over the world." When they play, you feel the love.

"An orchestra musician is an artist, not an employee, and artists must be given the chance to take initiatives and to be creative," says Fischer in his mission statement. "Only an orchestra of true artists – making music as a highly disciplined team – is able to realise the dreams of the composers and pass on an uplifting experience to the audience, touching all listeners deep in their heart. This is our aim for which the Budapest Festival Orchestra has been created."

Fischer insists that in devising his Audience Choice events he is not setting out to create a new concert experience.

"Oh, it is certainly not my desire to invent new concert forms," he says. "We have first rehearsals with the orchestra all the time and we love them. Now we simply invite the audience to take part in that experience."

But for the audience, there cannot help but be a difference. Imagine going to the cinema, knowing in detail the story of the film you are about to see. Many audience members know "the story" when they go to concerts, and when surprises are mostly limited to the interpretation of a familiar work, the threshold between enjoyment and autopilot can often shrink. There is an extra thrill in turning up not knowing what we will hear – but there is an even stronger one, perhaps, in knowing that the orchestra doesn't know what it will play. Won't it end up as one big mess? Not with these musicians, it won't.

The Budapest Festival Orchestra and Ivá* Fischer perform at the BBC Proms, Royal Albert Hall, London SW7 (0845 401 5040) tonight (main concert 7pm, Audience Choice Prom 10pm)