Then this week, photographs showed Katie sporting what looks suspiciously like a new nose. Coupled with a change of hair colour from streaky blonde to glossy brunette, she looks altogether softer and more sophisticated; not a child-woman or blow-up fantasy doll but a real grown-up.

In her private life, Jordan and Katie have always been separate. Jordan is the character Katie created to be her brand name and also to carry her emotional baggage, which is considerable.

Katie’s early experiences with men were not happy, not to say disturbing. Her father Ray Infield left when she was four (Price is her stepfather’s name).

Two books have made millons

When Katie was seven, she was molested while playing in a park near her home in Brighton by a man who dragged her into the bushes. On another occasion, still in her childhood, another man tried to pull her into his car.

As a child model of 13, a photographer made her strip to her underwear; the man turned out to be a convicted paedophile who had plastered pictures of the pubescent Katie all over his house.

Katie’s first proper boyfriend, to whom she lost her virginity when she was 16, was 11 years older and beat her up. She has since admitted suffering violence “to some degree” in subsequent relationships. The next boyfriend undermined her confidence by comparing her unfavourably to Pamela Anderson but didn’t like it when she got implants.

Peter is also her partner in showbusiness

She became pregnant by footballer Dwight Yorke, who promptly dumped her and has played little, if any, part in his son’s life.

If being a sex object was all she was good for – as the men she met told her – then she would exploit it; she would, via Jordan, be the richest, most successful sex object ever.

Jordan is a hard worker and Katie is a formidable negotiator. Jordan became famous enough to be invited on to I’m A Celebrity…Get me Out of Here! in 2004. She didn’t win but she did fall in love with jungle-mate Peter Andre, the Australian singer of a Greek Cypriot family who is now her partner in life and in showbusiness.

And it gave Katie Price the opportunity to step out of Jordan’s shadow.

Katie loves horses and dogs. She is also a devoted mother to her children by Peter – Junior, two-and-a-half, and baby Princess Tiaamii, five months – and Harvey, her son by Dwight Yorke, who is virtually blind, autistic and needs constant care. Nannies come in when his parents are working but they do not live in; Katie and Peter take over at the end of their working days, which are invariably packed.

As well as the modelling there are meetings about future product launches – her own beauty and bed-linen ranges are in the pipeline.

There’s the writing – OK, there is a ghost-writer, Rebecca Farnworth, who penned her novel Crystal, but Katie still has to give her an idea of what to write. There’s the Osbourne-style, at-home documentaries and their new chat show. They are also just breaking into TV in America, where Katie’s accent and singular idiom make subtitles necessary (though viewers apparently have no trouble understanding Peter’s Australian accent).

All this is happening under the name of Katie Price. The full form of address may still be “Katie Price, also known as Jordan” but the scales, for the moment, are evenly balanced. It is surely inevitable that it will soon change to “Katie Price, FORMERLY known as Jordan” and then Jordan will be eventually left out altogether.

Credit is due to Peter for facilitating this shift in image and it is worth noting that he calls her Kate, which sounds more mature than Katie.

She’s 29 and she hasn’t finished with plastic surgery by any means, which will not endear her to the feminists. But Katie Price is playing a much longer game.

What’s the betting that we’ll still be talking about her when she’s a very glamorous pensioner?