Susan Lawton was having a pleasant alfresco lunch with her daughters Sophie and Sarah on Tuesday when the man at the next table began behaving oddly – first shouting about football before singing Ode to Joy and then joining about 50 other people in an impromptu song and dance routine.

"We were a bit confused to be honest with you," Lawton said after the experience in Covent Garden, London. Someone did come over with a bit of paper "but we thought he might want money so we ignored him", she added.

The Lawtons, from Bromley, south London, had witnessed a rigorously rehearsed Shakespeare flashmob which kicked off a week of pop-up performances across the capital in a project created by the actor Mark Rylance.

It began at 2pm with two men shouting about football across the cobbles of Covent Garden. The first man on a balcony, a countertenor, then broke into "Full fathom five thy father lies", the song sung by Ariel in The Tempest.

The second responded by singing Ode to Joy from Beethoven's ninth. Then a full flashmob joined in with about 50 performers in silly wigs singing songs.

"We didn't really know what was going on," admitted Lawton. "What were the wigs about?"

It was a valid question but the daftness was, in truth, more of an appetiser for the main event which involves the actors stopping people and delivering lines in character – whether Banquo, Hamlet, Cleopatra or Puck.

The actors will be in ordinary clothes and Rylance said it was all about Shakespeare's lines sounding like they were coming from real people: "The real meat of the project is the infiltration and the ambushing that's taking place. We hope it will be an unusual and memorable experience for people."

Of course not everyone will hang around for the whole "o, my offence is rank" let alone "to be or not to be".

"But even one line of speech can still be something you can bounce around in your mind and in your soul," said Rylance.

"The actors will also be changing the meaning of what they are saying depending on who they are talking to and how they win that person's confidence to listen. The actors are finding out how to win and woo an audience to stay and hear something."

The pop-up project has been directed by Jonathan Moore who deliberately cast his net wide for actors.

"Theatre shouldn't really be – and it tends to be too much – white, middle-class Oxbridge types speaking in posh voices," he said.

"That idea of playing Shakespeare is actually quite a recent one – there were lots of different flavours and sounds and tones to the way Shakespeare was performed in the day."

That means the cast is aged from 17 to 70 and features able and disabled actors.

"A lot of them are, unfortunately, not actors who you will see at the Globe or the RSC, they have a much more individual approach," said Rylance, who is performing in Richard III at Shakespeare's Globe.

Moore said there was a lot to be said for the element of surprise. "It was important to us that it is a democratisation of Shakespeare. When you are least expecting something, you're kind of more open to it in a strange way. Your defences aren't up."

There will be five more What You Will events at different places in London, the last one on Sunday. All of them will be a surprise, although people can register at www.molpresents.com/surprises for updates. The project is being staged as part of the London 2012 festival, the finale to the Cultural Olympiad, and people can record their encounters with the performers on Twitter using #shakespeared.

All of the initial responses on Twitter were positive. "Meeting some amazing people quoting shakespeare! They were all so good!" tweeted Rosie McCarthy.

"Just got #shakespeared in Covent Garden. He was v good. Thanks #London2012," wrote Eleanor Banks.