But whatever the rights and wrongs, it was evident by the start of this year that her romance with Hugh wasn't working, and so she told him they should accept it was over and move on.

But all was not as it seems. For it's looking increasingly like Jemima regarded the dumping as a neat piece of brinkmanship that would bring Hugh to heel.

For amazing though it may seem, she was keen from the outset to revive this fraught relationship - even though many of her friends and family were delighted it was over.

And it seems that, in some ways at least, her strategy has worked.

"Hugh would love to get back together properly with Jemima and they have been again discussing getting married," says a source.

"It is very much part of the deal that if they can resolve this crisis, then it will lead to marriage and children. They both say they want that, so it is a question of whether they are able to work it out."

The friend added: "I stand with a lot of Jemima's friends who don't like Hugh. I don't honestly think that the relationship has ever been happy.

"But she desperately wants him back in her life, and he desperately wants to be there. Quite how it will pan out, I don't know - and I suppose, in all honesty, neither do they."

The break-up, therefore, has proved as complex as the relationship. They are, it transpires, still an item in many significant ways.

Both regard themselves as boyfriend and girlfriend and are seeing each other as secretly as they can manage in a bid to work things out.

They were annoyed but also amused when they were "caught out" on one of these dates at the end of March.

More recently they had a twohour lunch in Notting Hill. There have also been other dinner dates.

A few days ago, Jemima was pictured entering Hugh's London home, where she remained for two hours before departing alone into the night.

Although we are asked by Jemima's people to accept that these are a "catch-up, and a giggle with no strings attached", in truth, Hugh has been wooing Jemima afresh and she has been delighted with the progress made so far.

It is suggested by friends that, despite this, the physical side of the relationship remains on hold, even though, as far as Jemima is concerned, Hugh is the man for her.

What, then, are we to make of her being pictured kissing and dating various eligible men-around-town?

For Jemima has twice been out with dashing bachelors who could surely provide her with more fun and companionship than Hugh ever did.

The first was Lord John Somerset, an old friend, with whom she enjoyed a jolly night out at a London club.

Despite her fondness for worthy causes, Jemima is very much a funloving, upper-crust girl, and a night out surrounded by braying socialites and heavy-duty cocktails is absolutely her scene.

She and Somerset (whose ex-wife, Cosima, is an old friend of Jemima's) looked an affectionate couple when saying goodbye on pavement in the full view of a phalanx of photographers.

That display, though, was all about public consumption rather than private passion.

She was again not shy of publicity when she attended a "Russian Rhapsody" dinner last week with the superrichbanker, and one of Britain's most eligible bachelors, Nat Rothschild.

Although they looked cosy at the table and were described by observers as "very touchy feely", they are categorically not an item either.

But how it must needle Grant to see the woman he apparently still loves kicking up her heels with some of the richest and best connected men in London.

The theory in Grant's circle is that these dates are Jemima's way of keeping Hugh on his toes. They also serve the purpose of putting the media off the scent of their revived romance.

It seems, however, that Grant doesn't much like this part of Jemima's strategy.

Despite the fact that they've played such a big part in making him both famous and wealthy, he detests the media, believing he ought to be above being bothered by such vile, ordinary people.

(He is said to have shrieked at the photographer Ian Whittaker last week: "I have millions! And you are just scum!")

He hates the sense that he is part of a soap opera, that his life is commented upon, and that his girlfriend is photographed with other men.

There is a sense of exasperation here for the actor; one society pal makes the claim that he feels "powerless", which is why he lashed out this week. This may not be that far-fetched.

The friend says: "The situation is that they are seeing each other, but they are not seeing each other. It's not easy for either of them."

However for now, apparently, Hugh will have to put up with the soap opera because keeping the renewed fledgling romance secret is a top priority - especially as it seems her family aren't really aware of what's happening.

So can this brittle pair work it out? The omens aren't good. All the problems which drove them apart are still there.

She is a social girl and wants someone who finds her endless whirl of parties fun rather than purgatory.

And although he says he wants to make the ultimate commitment to her, one wonders if psychologically he's the kind of man who can commit totally to another person.

They are, as a source pithily remarked: "Miserable together; miserable apart."