She has fitted bras for the great and the good for 40 years but June Kenton, owner of the iconic lingerie boutiques Rigby & Peller, is finally hanging up her bra straps at the age of 73.

Founded at the beginning of the Second World War, Rigby & Peller soon won favour with royalty — its most famous customer is Queen Elizabeth II — and today it is equally renowned among rock royalty. Lady Gaga is wearing Rigby & Peller in her latest music video. Gwyneth Paltrow, Margaret Thatcher and Sophie Dahl are all devotees.

From staid to stylish

Yet, the brand hasn't always enjoyed such fashionable success. Before June took over Rigby & Peller in 1982, the label was considered old-fashioned and staid but June could see the potential.

"What really appealed to me was that Rigby & Peller only did made-to-measure underwear, so it would allow us to make whatever our customers wanted ourselves. Up until then, we could only do alterations," she explains.

"Of course, back when Rigby & Peller started in 1939, a made-to-measure service was much more important, as you just couldn't get bigger sizes. When I first began working, the biggest cup size you could buy was a C.

"Even when my husband, Harold, and I first started selling lingerie in our own shop in the Seventies, sizes only went up to a D. Now sizes go all the way from A to J."

The shop also came with royal responsibilities — Rigby & Peller has held the Royal Warrant of Appointment as Corsetieres to Queen Elizabeth since 1960.

This meant that one of June's first tasks after taking over the shop was to visit Buckingham Palace to fit the queen.

"I was terrified. I was so nervous I couldn't sleep or think straight," she laughs.

June is used to people asking her what it's like to fit the queen but on this subject, her lips are sealed. "When you go into the fitting room with any customer, you are at one with that person. You become their confidant. Sometimes they will tell you their life story but what they say behind that curtain remains confidential, whether they are the Queen, Princess Diana or anyone else," June insists.

She thinks this is partly why Rigby & Peller has become the lingerie of choice for today's celebrities. "We are very discreet and never reveal anyone's measurements, which, I think, appeals to our famous customers," she says.

Young appeal

Of course, Kenton's flair for PR and design also helped to revive the brand's fashion credentials. "I focused on making it into a younger, more upmarket brand, designing our own ranges and branching out into swimwear.

"But what makes us unique is that we have never forgotten our commitment to fitting and service. We take care of all our customers in exactly the same way — famous or not," she explains.

She is convinced that a good bra is a key to good health. "Young girls are getting larger bosoms. I'm not sure why but it means that being fitted with a good bra is even more important. Otherwise, they will be too shy to go running.

"The problem is that their bras are being chosen by their mothers, who have also never had a bra fitting. My mother always took me to be fitted for my bras when I was young but now people just pick them off the rack."

June is on a mission to change our ways. She says: "Wearing the right-size bra boosts your confidence and makes you look smaller. What I do can really change someone's life.

"Sometimes, you might have to try on 15 bras before you find the right one and because all bras are different, you can't rely on measurements alone. In our fittings, we never use a tape measure, only sight, as what might fit in one cut of bra won't work in another."

While improving body image for healthy women is laudable, June has always made sure that Rigby & Peller was sympathetic to the needs of women with breast cancer too, something that became even closer to her heart two years ago when she was diagnosed with the disease and had to have a mastectomy.

"I was lucky. I had an implant done at the same time as my mastectomy but I've always believed that just because a woman has breast cancer doesn't mean she can't have a fashionable bra. After a mastectomy, you are only a few hours older, so you shouldn't be treated like an old woman and forced to wear some hospital appliance instead of nice underwear," she explains.

Since starting in the clothes business by helping out in her father's shop after she left school, June has seen lingerie change beyond belief.

"Control garments today are amazing. They're lightweight and gently pull you in. My mother always wore made-to-measure corsets and they were so heavy and bulky that when she washed them, they took two days to dry."

The 200 drawers of rainbow-coloured bras that line each of her stores are a far cry from those early days, when, if you needed a larger size, you were stuck with what June dismisses as "fuddy-duddy" styles. Now, whatever your size, you can have a pretty bra in any colour you want," she says.

While June will continue to fit her most famous customer, she now plans to take on a more ambassadorial role, having handed the company reins over to her son, David.

And, with 85 per cent of women wearing the wrong bra size, it seems there is still plenty of work to be done.