“My legs are a bit trembly – like after you’ve had a sudden shock,” says Naomi Alderman, without realising the pun she’s just made.

We are in the green room at London’s Festival Hall where, just a few minutes earlier, Alderman was announced as this year’s winner of the Baileys Women’s Prize for Fiction for her sci-fi novel The Power.

Her gripping book – described by the judges as a “brilliantly imagined dystopia” – explores a future in which women have the ability to give electric shocks at will – often with deadly results – and men live in fear.

When I suggest that it all that sounds a bit like a plotline from Doctor Who, Alderman nods enthusiastically.

She did, after all, write a Doctor Who spin off novel starring Matt Smith’s incarnation of the Time Lord in 2011.

“I would love to write for Doctor Who on the telly – and you can put that in this piece!” says Alderman. “That has been an ambition of mine for decades.”

She recalls how her first ever rejection letter was from Doctor Who magazine when she was 14. “I still have it proudly. I was very thrilled because a rejection letter is what proper writers get.”

But back to our interview about The Power.

What ideas inspired the novel?

One of the ideas of the novel is that women – if we could be in a position to physically hurt people – would be all lovely all the time. I think that in itself is something of a patronising idea.

Given that women can be CEOs how did we ever end up in a position when we thought they couldn’t? The answer seemed to be to be very much tied up with violence.

On average men are taller and have more muscle strength in their upper bodies. On average more men could hurl a women across the room than vice versa.

There are many wonderful men in the world, but it only takes one man in a thousand to be exercising that [power] for every woman to end up afraid. At the point you are afraid your options are gone.

That’s my theory about what’s going on.

How hard a novel was it to write?

A wrote a full draft of 200,000 words and then threw it away and started again. I started with just one narrator, and then re-wrote a draft with four main characters.

The book is dedicated to your mentor Margaret Atwood and her partner Graeme Gibson. How much an influence was she?

The first draft was written talking to her as I went along. We had long conversations about what the world might be like if this had happened. When I reached the point of the second draft I realise I had got to write this next draft without showing it to her, I think that was the right decision.

You’re adapting The Power for a TV series. How is that going?

I’m in the process of writing the pilot right now. Its been a joyful process of thinking about what else might enter into that world as there’s much more space in a long-running TV show.

The time scale is a bit finger in the wind. I’d hope I’d have a draft of the script written in the next few months.

How different are the reactions from male and female readers?

Women get very, very excited by this book. They understand what I’m talking about, Men look at me with tremendous fear.

I think the reason is that it’s very different to know that violence happens to women in the world, than it is to consider what it would be like if you had to be afraid of that violence yourself.

It’s very different to see someone with a gun pointed at their head than when the barrels are pointed at your own head.

I’m quite pleased that I’ve given men that experience to see this would be really terrifying – and they wouldn’t be able to live their life in as free a way as they do.