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Talk about making an entrance. Early on in the first episode of NBC’s One Big Happy (Tuesdays at 8:30/7:30C, premiering this week), Kelly Brook appears completely starkers, her private parts blurred for TV.

Her character, Prudence, is the furthest thing from a prude, and that unnerves her new roommate, though it delights her new husband. In a modern twist on the old Three’s Company premise, Brook plays the new point in a domestc triangle: newly married to and in love with Luke (Nick Zano), who saved her from being deported back to the UK, she discovers that he lives with his lesbian BFF Lizzy (Elisha Cuthbert), who announces she’s pregnant with Luke’s baby. It’s funny stuff (Ellen DeGeneres is a producer) and an auspicious debut for the curvy British import.

She recently opened up to us in a candid conversation that ranged from nudity to dating to favorite cocktails.

“Nudity doesn’t faze my character. To her the fact she’s naked is irrelevant. Everyone else’s attitude towards her being naked is what the issue is, but she’s fine with it herself.”

How did you get the role on One Big Happy?
I live in England, and I have a lovely life there: A nice home, regular income, good jobs and lots of endorsements. My manager always said, ‘Come over for one pilot season. I know something will happen.’ I didn’t know if it was the fear of rejection or what, but I didn’t. But they sent me the script and I immediately loved it. It was so funny. And the character was so fun and warm. She’s lovely and feisty and positive. I loved the dynamics of the character. So I had to come over and try to get the role.

Did you see yourself in the character? What grabbed you?
A hundred percent. I really connected with her on a personal level. Prudence is British and is a free spirit and she travels around. She’s never quite found a life partner or anyone to keep her to one place for too long. She meets Nick randomly in a bar, falls madly in love—it’s a whirlwind, really. Then she gets the shock of finding out Lizzy is pregnant. I don’t think she even realizes half the time that Lizzy doesn’t like her.

She has no problem taking her clothes off or dressing sexy.
It doesn’t faze her. To her the fact she’s naked is irrelevant. Everyone else’s attitude towards her being naked is what the issue is, but she’s fine with it herself. In real life I dress very conservatively.

How do you feel about walking around nude, albeit pixilated?
In my career, I’ve modeled lingerie, I’ve posed for Playboy. I was in Piranha 3D in a bikini, but I was nervous because I’m older now, and also you think: Are people going to take me seriously? Is it just going to be focused on that? But she’s such a fun character and I could see that it was going to be a really interesting journey.

How did you get started in show business?
I’ve been acting since I was a kid, in school plays and whatnot. At 11, I said to my mom, ‘I really want to go to a full-time performing arts school,’ and she indulged me and took me for an audition. I was from a small town outside of London and I ended up getting on the train every day, two hours there, two hours back. I went to a performing arts college and then I left at 16 and started working in TV. I did a little bit of modeling but mostly television. I worked on The Big Breakfast, which was an early morning TV show. I got that job at 18.

You did a movie, Taking Stock. Details?
It’s a British independent film. It’s a comedy. I play Kate. She is down on her luck. She loses her job, a boyfriend cheats on her and she becomes obsessed with Bonnie and Clyde. And she decides it’s not really paying off being a good girl. So she decides to be a bad girl and organizes a heist. It was great to find a great female lead character like that in a comedy.

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Yes, Ms. Brook has her own line of swimwear. It’s just one of many at kellybrook.com.

What do you think of American men? Are you dating over here?
I’m not dating. I’m open to it, but I’m so busy with the show and everything. It’s not really been anything that’s come my way. I really don’t go out to bars or anything. It’s hard, you know. I’m 35 years old and where do I go meet someone, Instagram? So I’m very much single.

What’s sexy to you in a guy?
A sense of humor. Someone that’s kind and considerate. Someone that’s loyal. And it helps that they have good guns. I’m talking about muscles here—I’m not endorsing guns!

How do you like guys to approach you?
Just talk to me. Just chat. ‘Hi, how are you?’ I’m not fussy. Show an interest, I’m all yours.

Where do you see your career going?
I love working in comedy. I would really love for this show to have an opportunity to continue, or I would love to do another series. Movies—I’d love to do some romantic comedies. I’d love to just stay in Hollywood. I love England, but I’ve done so much work there now it’s nice to come here. And the weather is absolutely gorgeous!

Besides acting, what are you passionate about?
I love dancing. I did the show Strictly Come Dancing, which is the U.K.’s Dancing With the Stars. My father passed away during the series so I left, but I got to week eight, so I did well. I like writing. I wrote an autobiography last year and there’s been talk about publishing it here. I got into interior design, decorating. I live in a 14th-century cottage in England, by a stream. It’s rustic. It’s not glam. It’s just very beautiful, magical and whimsical.

Since you own a bar [London’s Steam and Rye], what are your favorite drinks?
A Moscow Mule. We have a drink called the Monica Lewinsky. It’s a creamy, frothy oral delight. Very popular, that one.