One is a small but well-regarded theatre in a leafy London suburb. The other is an edgy venue in one of Tel Aviv's least salubrious neighbourhoods and wouldn't fit most people's definitions of a theatre at all.

This June marked the second collaborative event between Hampstead's New End theatre and the Karov theatre, located in a corner of Tel Aviv's New Central Bus station.

The partnership began last summer, while Alexa Christopher-Daniels, the New End's associate artistic director was in Israel working at Karov.

For Christopher-Daniels, it was never an option to leave Karov behind when she returned home.

"I loved the purpose of it so much," she says. "It's all about bringing audiences closer to what they are watching. At Karov you have this real sense of action, there's no line between the process of creating and watching."

She and her Israeli counterpart Dorit Nitai Neiman would endlessly discuss how they could "bring Karov beyond Karov". There was always the option of translating a play from the Hebrew, but they wanted a project which would go further and bring people from both countries together by way of a shared experience.

The obvious answer was with the SHE festival, a regular event created by Neiman in 2006, blending improvisation, music and dance with strong social messages and involving an all-female cast and a post-show discussion session.

Neiman had long wanted to take SHE beyond Karov; as Christopher-Daniels says, "It all just slotted into place."

In October, Neiman visited the New End to prepare for the London SHE festival, which took place in March. They assembled a cast of three Israeli actresses and three British-based ones, and set to work.

It wasn't without challenges – SHE festivals involve groups being taken by male actors around "rooms" for eight minute "scenes" – doable in the eccentric Israeli space, more complicated in a cramped and traditional 84-seat theatre.

"Our audiences generally wouldn't squeeze backstage and be climbed over with a torch," admits Christopher-Daniels. "We completely changed how people were used to looking at the theatre."

Obstacles aside, the British festival was every bit as colourful as its Israeli predecessor – one scene involved a woman reciting a monologue to her pillow, another saw audience members unwittingly seduced by an actress singing to herself. Like interpretative arts events around the globe, it was unusual, bold and modern.

But for the women behind it, the SHE partnership is about more than pushing creative boundaries; it was a way to take the phrase "Israel and theatre" beyond shows like Seven Jewish Children.

"It's about Anglo-Israeli ties, cultural ones rather than the political," says Christopher-Daniels. "This is a way to raise awareness of why Israel should be a part of world theatre without making an overt political statement."

The plan is to take now cross-cultural SHE festival back to London in February 2012. Christopher-Daniels wants to see it expand to Edinburgh; Neiman has ambitions for all around the world.

"It's a very exciting as to how it might develop. It's not just about Dorit and I, or two theatres," she says. "The SHE festival is an ongoing thing and the ties can only get stronger.

"I want to show the world how two cultures can come together with dynamism and excitement," she adds. "Maybe only a small world to begin with, but it's a start."