Judy Blume, tiny and smiley and as warmly open as befits the author of seminal novels about growing up Forever…, and Are You There, God? It's Me, Margaret is sitting in a hotel in London and talking about the hate mail she has received. It comes, she says, every time she speaks out on behalf of Planned Parenthood, an American pro‑choice group for mothers.

"I went to a couple of places two years ago and I got seven hundred and something hate-mail warnings – 'We know where you are going to be and we'll be there waiting for you', that sort of thing," says Blume. "My publisher sent me with a bodyguard. He was wonderful, I loved knowing he was there. And nothing happened and probably nothing would have happened, but it was very scary."

It is an incongruous revelation. Blume, 76, is the sort of author who is beloved by her fans, who stretch from the children of today to the adults who read her books when they were growing up, and were astonished at finding a novelist who spoke so clearly, so uncondescendingly, so directly, to their concerns, whether masturbation (Deenie), periods and boobs (Margaret), sex and birth control (Forever…), or death (Tiger Eyes).

Her books have sold 82m copies worldwide since The One in the Middle Is the Green Kangaroo, her first book, was published in 1969. She has been given an award for lifetime achievement from the American Library Association, the Library of Congress living legends award and the 2004 National Book Foundation medal for distinguished contribution to American letters. But Blume is also the recipient of a more dubious accolade: she is one of the most frequently challenged authors of the 21st century. Her books have drawn fire from parents ever since the 80s for their frank depiction of puberty and sexuality, from Deenie, the 13-year-old who touches herself in "this special place and when I rub it I get a very nice feeling", to Katherine and Michael, the teenagers who fall in love and have sex – ever so responsibly – in Forever ….

"Deenie, Forever …, every year, somewhere, they're challenged," says Blume. "When I started, in the 70s, it was a good time for children's book writers. Children's reading was much freer than in the 80s, when censorship started; when we elected Ronald Reagan and the conservatives decided that they would decide not just what their children would read but what all children would read, it went crazy. My feeling in the beginning was wait, this is America: we don't have censorship, we have, you know, freedom to read, freedom to write, freedom of the press, we don't do this, we don't ban books. But then they did."

Blume's theory is that children read over what they aren't yet ready to understand. Sometimes, she says, "kids will actually go to Mom or Dad and say 'What does this mean?', which is the perfect time to talk to them about it. But that's when sometimes parents get hysterical. Really. It's like, 'Argh, I don't want to talk to you about this, let's get rid of this book, I don't ever want to talk to you about this, I don't ever want you to go through puberty.'"

Are You There God? It's Me Margaret by Judy Blume

Blume most famously tackles puberty is in Margaret, her story of a sixth grader who talks to God like a friend, worries about being the last to get her period, and longs for breasts. "Are you there, God? It's me, Margaret. I just did an exercise to help me grow. Have you thought about it, God? About my growing, I mean. I've got a bra now. It would be nice if I had something to put in it."

"There's a lot of me in Margaret," says Blume. "I talked to my own private God the way Margaret does. I would plead, 'Just let me be normal', which meant let me have my period, give me some breasts, and hurry up ... You know, the 50s, the body image for women was round and curvy, and I was this skinny little thing, very small, and I wanted to be round and curvy the way round and curvy women today want to be skinny things."

"Everybody who writes fiction draws from their own life, but if it ended there, it would be very boring," she says. "When I talk to kids and they say, 'How do you become a writer?', well, I don't know that you become a writer: you just are. I always had stories, they were always there inside my head. I never told anyone, but they were there."

She trained as a teacher but never taught; she was married before she graduated from college. "It was ridiculous, [the idea] that any marriage would work that starts that early, before you have any idea who you are." She recalls: "It was the most traumatic time of my life. My father had just died and the wedding was scheduled. I was 21, we got married and I did my final year at college. Then, before that ended, I was pregnant, and had two babies by the time I was 25, and then started to write."

She'd make up rhyming stories when she was washing the dishes at night and added her own illustrations, sending them off to publishers. Then she decided she wanted to write novels, took a writing course, and out came Iggie's House, the story of Winnie, a girl whose quintessentially white surburban-American street gets its first black family, and who is confronted with – and confronts – racism.

"Writing saved my life," she says, seriously. "It saved me, it gave me everything, it took away all my illnesses. I loved having little kids, I relate to little kids, but something was missing, and I don't think about this every day, but when I think about it, it's that creative energy. I was an imaginative, strange little girl, and in school I had a lot of creative outlets. I danced, I sang, I painted, there was a lot of that, and suddenly I didn't have any of that. I've thought about this – I think that's why I was having such a bad time. And there was the marriage, too, but that's another story." Her marriage, she says, lasted 16 years and "we're very good friends now. But it was very tough, and I felt lonely and didn't have the friends I had when I was in school. I missed that female friendship." She left, along with her children, in 1975. In 1976 she married again, and moved to New Mexico, but the marriage didn't work out. She has been married to her third husband, George Cooper, since 1987.

Blume talks a lot about friendship, female friendship – as well as George, her best friend, Mary, is here in London with her. It's a key theme of her novels, too – Summer Sisters; Here's to You, Rachel Robinson; Just As Long As We're Together.

What followed Iggie's House was an extraordinary period of creativity: between 1970 and 1977 she published most of the books she is now most famous for, including Blubber; Tales of a Fourth Grade Nothing; Then Again, Maybe I Won't and Starring Sally J Freedman As Herself, her most autobiographical book. "I was very prolific in those years ... I was young and I remembered everything. I had total recall," she says. "I think I wrote Margaret in six weeks; now it's like four years. It was spontaneous, it just poured out. And in the middle of that I was writing the Fudge book."

Fudge, the naughty toddler who drives his brother Peter wild, was originally drawn from her son; Forever…, she says, was written after a request from her teenage daughter (it's dedicated to her: "For Randy as promised … with love"). "She was reading all these books, where a girl succumbed [to sex], she would be punished, sometimes she would die. And Randy said, 'Couldn't there ever be a book where two nice kids do it and nobody has to die?' And I thought 'Yes, I need to write this'."

Blume's protagonists range in age from toddler Fudge to the adult Caitlin and Vix of Summer Sisters, but perhaps her best work centres on the crossover from child to teenager, whether it's Tony; in Then Again, Maybe I Won't, making sense of a world where his friend is shoplifting, or Margaret. "I love the cusp," she says. "I always wanted to write, but I wasn't interested in writing about teenagers, because, looking back, I felt teenage Judy was very boring and bland. It was the 50s, and I hated the 50s. We all just wanted to fit in and none of us, not even with a best friend, were willing to go deeper. The 50s was such a time of 'Pretend everything's OK, pretend it's all good.' Our parents had just come through the war, everyone just wanted their families to be happy, we didn't want to rock the boat."

The younger Judy was more interesting, she thinks. The family hadmoved to Florida when her brother was sick, leaving her father, a dentist, behind in New Jersey. "I was making all kinds of bargains with God, feeling that I had to protect my father ... I adored my father, not only worried about him flying, which was a very scary idea, but worried about him being safe. It was a bad year, and I became ritualistic. I took on the burden of feeling responsible for his wellbeing, at nine, but never telling anybody. God, what a burden, when I think about it now, for a child."

Blume's recall of her childhood is exact. She says she finds it easy to "connect with children, to see their side of the story". "I'm very attached," she says. "I don't know why. I think some people just are. And I don't think it's necessary to have children to be like that. Maurice Sendak never had children but he was so connected to the child inside that he never lost that."

She's currently working on a new novel for adults, her first since 1998's bestselling Summer Sisters. The untitled novel is set in the 50s, partially, in Elizabeth, New Jersey, where Blume grew up, and sees her tackling again a topic which preoccupies her – young pregnancies, and young motherhood. One of the main characters has a baby right after high school, and never tells the father.

"I come back to that again and again – what if, what if – it could so easily happen," she says. "It was a very scary idea that you could get pregnant, and three of the best girls in my school were pregnant, at graduation, and it changed their lives. There was no abortion, you know. Yes, some girls got shipped to Aunt Betty's house in the country and came back without a baby, and some girls had a hasty marriage."

"I think we got married young because we wanted permission to have sex, all the way sex, and so yeah, we all got married young, my generation. Our parents didn't because they came of age during the depression, they had one, maybe two children later. My mother was 34 when I was born, which today is nothing, but in my generation that would have been old. We rushed into marriage and having children before we had any idea what we were doing."

When her American publisher announced publication of the new novel in summer 2015, the news was greeted with rapture and covered by outlets from Time to the New York Times. An earlier New Yorker piece called her books "talismans that, for a significant segment of the American female population, marked the passage from childhood to adolescence".

Blume's younger fans have poured their hearts out to her for years – she even published a book of their letters, and had to go to counselling to learn "how to be supportive without feeling that I needed to save them". Her adult fans recall her as the author who understood. "It's hard to understand, now that YA fiction is so widely written and accepted, that in the early 80s no one else wrote like Judy Blume," says novelist Charlotte Mendelson. "It wasn't only that her protagonists were funny, and sympathetic; they lived in a totally recognisable ordinary world, and had real, painful, modern problems; reading them made one feel much less alone. She signed a copy of Deenie for me recently, and my joy was uncontained."

The musician Amanda Palmer has even written a song about Blume: "You told me things that nobody around me would tell ... I don't remember my friends from gymnastics class, / But I remember when Deenie was at the school ... Margaret, bored, counting hats in the synagogue ... All of them lived in my head, quietly whispering: / "You are not so strange." (Blume loves it: "She's sitting at the keyboard in her bustier and garter and she's singing this song, it's so beautiful.")

Palmer says she'd struggled for years to name her "influences", when asked by journalists, "and then it hit me: I totally forgot about Judy Blume. As I traced myself back, I realised that she'd opened up all these emotional doors and windows that started off locked, and I'd taken it totally for granted. It was such a eureka moment that I had to write her a song. And thanks to Twitter, she heard it. I cry pretty much every time I play it."

Teasingly, Blume says right at the end of the interview that she's now planning, sort of, a memoir up until the age of 12; she's not, she ends by chuckling, "going to do a Philip Roth" and announce her retirement.

"George just read me a really funny one [a blog in the New Yorker], it was, 'Ladies and gentlemen, Philip Roth has announced he has eaten his last sandwich.'" She laughs. George is waiting. She heads off to enjoy London.