Mrs Dursley is sitting on the sofa in the living room of number four, Privet Drive. She is wearing pearls, a cardigan and has one leg elegantly tucked behind the other. The furnishings are salmon pink, the carpets are beige and her lips are pursed in disapproval.

Then she opens her mouth, speaking with an Irish lilt rather than a Surrey accent, and laughs with un-Dursley-ish good humour, and suddenly it is the brilliant actress Fiona Shaw sitting in front of me, rather than Harry Potter’s ‘perfectly normal, thank you very much’ Aunt Petunia.

Fiona is at Warner Bros. Studio Tour London to celebrate the opening of the interior of Privet Drive to the public for the very first time.

Up until now visitors have only been able to admire the well-manicured lawn of number four. But for 10 days, from the 27 May, visitors will be able to see inside the suburban house and witness the chintz up close.

Fiona looks incredibly at home on the clean but rather dilapidated sofa, and we are surrounded by thousands of letters inviting Harry to attend Hogwarts School of Witchcraft and Wizardry. When Privet Drive opens to the public, a device created by the special effects team will spit the letters out at visitors – who may even be lucky enough to take a copy home as a souvenir.

‘It was great fun being in Privet Drive,’ Fiona recalls. ‘It was just Richard [Griffiths, who played Mr Dursley], Daniel [Radcliffe], Harry [Melling, who played Dudley] and I. We were quite sealed off from the others [on set].’

It has been 15 years since Fiona first walked into the house, with her hair in curlers, and shook off her amiable exterior to become Harry’s buttoned-up and fiercely house proud relation. It might look like an ordinary bricks and mortar house, but it is actually made from fibreglass.

Privet Drive was a prison to Harry for years, but what was it to Mrs Dursley? ‘It was absolute bliss for her,’ Fiona tells me. ‘This house is incredibly aspirational. She probably would like a bigger house but this is all she could manage so she manages it really well. She decorates it within an inch of its life and works very hard at keeping it clean.’

Our conversation turns to the late actor Richard Griffiths, who played Fiona’s on-screen husband Vernon Dursley. ‘He was a wonderful actor and a wonderful person,’ she says. ‘He was very talented: he knew a lot about calligraphy, he knew a lot about history, he was terribly well read. So he was a very good person to be around and a wonderful influence on Harry Melling and Daniel Radcliffe because he knew so much about everything.’

Mrs Dursley is quite a difficult character to empathise with: she is cold, uptight and rather cruel to Harry. When Fiona first donned her Marigolds in 2001, some of the later Potter stories had not yet been published, so she wouldn’t have known about Mrs Dursley’s childhood jealousy of her witch sister and how she’d even written to Hogwarts asking them to admit her.

‘We didn’t know that story yet, but funnily enough,’ says Fiona, suddenly animated and raising her voice, ‘it coincided exactly with my feeling which was that I wanted to be a witch!

‘I used to hope and hope that I would be [a witch]. In some of the scenes I remember playing the fear, the terror of letters arriving, the hatred of it. It was absolutely the hatred of envy. It really was. And I had it myself because I wanted to be in Hogwarts. I was very envious of all the witchcraft people. But that’s what the whole thing is built on. There should be another book about Mrs Dursley and how one day she went to a school called Hogwarts and found her redemption,’ she jokes. At least, I think she’s joking…

When I ask Fiona which non-Muggle character she would play in the films if she’d had the chance, she answers without a moment’s hesitation: Professor McGonagall. ‘I think she’s a great witch.’

In Fiona’s mind, Mr and Mrs Dursley represent insurmountable normalcy. They might pride themselves on being perfectly ordinary but they are designed to ‘trigger how awful it is to be only in the world’ and to represent ‘how much people always want something more’.

But however normal Mrs Dursley might think it is, entering Privet Drive is incredibly exciting. Later this month, some of the costumes worn by the Dursleys will also be on display at the Studio Tour for the very first time. Judianna Makovsky, who designed them, says the family were the most fun to dress, having to make clothes that appeared out of date and pretentious for Mr Dursley, and make some hideous jumpers for young Dudley.

Fiona’s favourite scene was filmed in the Dursleys’ living room. It is the moment Harry’s invitations to Hogwarts shoot out of the fireplace in a great plume of paper and green ink. ‘I loved it because it was full of both magic and very human nonsense.’ There was a man sitting in the fireplace and he had a catapult and fired the first letter. And of course he kept not shooting it to the right place. So we had to keep doing it.’

A very serious expression passes over her face and for a moment she is Aunt Petunia again. ‘So now I’ve ruined the magic,’ she says. Not in the slightest.