My wife says you can always tell a self-portrait by the quality of its self-regard. There’s something about the eyes and mouth (though not invariably flattering or admiring) or the set of the chin that give the artist away. Perhaps it’s simply that the artist is more interested in depicting the self than anyone else; or that the degree of self-awareness is inevitably deeper. Some of the great paintings have been self-portraits, from Rembrandt to van Gogh, and when they’re good they’re always worth looking at. So it was with optimism in my heart that I made my way to Kings Place to view the results of the second bi-annual Ruth Borchard Self-Portrait Competition.

In the late 1950s, Ruth Borchard (1910–2000) initiated a collection of self-portraits by contemporary artists that eventually numbered some 100 items and included paintings or drawings by Roger Hilton, Euan Uglow, Peter Coker and Anne Redpath. Borchard wrote to her chosen artists and offered them up to 21 guineas for a self-portrait, the fee varying according to their celebrity. Her intriguing collection has been kept together, and her family has inaugurated a £10,000 prize in her name. The winner this year is Thomas Newbolt (born 1951), with a painting replete with intimations of mortality, his face a sharply angled yellowish skull beneath green-tinged skin, below a purple hat; would that the rest of the exhibition were as good.

Inevitably among the 120-odd exhibits there’s a lot of earnest self-dramatisation, but there’s also far too much dreary attitudinising and a plethora of really dreadful painting. If this is the cream, what on earth was the rest of it like? There’s quite a spread of styles, as expected in our pluralist age, from the literalist to the expressionist by way of the symbolist and photorealist. It seems as if a lot of artists today when confronting themselves create masks of anonymity to hide behind. Or else fill up a lacklustre image with pin-boards of excess information. The greatest and most depressing shortfall is in character: both in painting style and human personality. The occasional glimmer of humour (see Sam Marshall’s etching as a fennec fox) is most welcome, likewise the even rarer trace of originality and imagination (as in David Freed’s forest of dreams in ‘Strange Season 1’).

The prices are huge (Ruth Borchard would have had a fit): few under £1,000, and at least a couple of dozen more than £5,000. I know artists have to live, but do any of these hopefuls ever look at the secondary market, where paintings are resold at auction in the low £100s? But despite all, there are a few fine pictures, including Peter Bowen’s pale and quizzical self-image; Diana Cumming’s wonderfully sensitive and decorative oil, line and colour arranged with refreshing pictorial logic; Robert Dukes partially reflected in a shaving mirror — a piercing glance of great frankness; Julie Held painterly and intriguing; a witty early drawing (‘Pre-Smokeless & Pre-Feminist’) by Michael Horovitz; Jane Joseph’s etching with Parthenon frieze; Mary Mabbutt’s typically stylised and rhythmic painting; a strong, moody drawing by Peter McGlynn, both concealing and revealing, inviting the viewer to engage rather than pass on; Shanti Panchal’s exquisite watercolour bending the rules by painting the artist’s muse; and Cherry Pickles reinventing herself as Dylan Thomas.

A trio of highly competent and not uninteresting artists represented by Flowers Gallery — John Kirby, Lucy Jones and Jiro Osuga — hangs at Kings Place almost as a reminder that Flowers is staging its own exhibition of self-portraits. Entitled Stranger, this claims the rather pretentious objective ‘to elevate the status of painting through the challenge of the self-portrait’. Of course, to a degree every painting is a self-portrait, containing as it does one individual’s response to a subject, which will never be the same as another’s. But when artists start looking at themselves, they either disguise things or reveal the state of their souls. By and large, I felt that the Flowers group played games with self-scrutiny, ranging from shape-shifting to burlesque, perhaps to avoid an uncomfortable analysis, or to sidestep the truth.

Among the best things here are Maggi Hambling’s lush oil, which spreads across a white canvas like a cloud of smoke, her features emerging from clots and curls and creases of paint, and then dissolving again; David Hepher’s ‘Self-Portrait with Graffiti’, tough and uncompromising, strangely haunting against its lurid background; while Tim Lewis, with his usual ingenuity, has created a machine which draws his profile on the wall when you turn a handle. Tony Bevan’s ‘Self-Portrait’ (2012), which has been used to advertise the show, is a congeries of decorative tattooing, burnt scarifications like pokerwork etching the lines of angst or tension in his head, and looks strong in the generally undistinguished company. On the evidence of this show and the Borchard, artists should be looking a bit harder at themselves or not at all.

Brief summer round-up: out of town there’s a delicious show of recent work by Stephen Chambers (born 1960) at the Wills Lane Gallery in St Ives, everyone’s favourite seaside art destination. Chambers is not only a colourist of unusual distinction, but also a witty commentator on the superficial intricacies of our everyday lives. His original take on the human condition also lends itself to deeper investigation, though he is not given to overt self-portraiture. His series of 20 etchings entitled ‘Trouble Meets Trouble’ has a resonance beyond its immediate appeal; on until 27 October, if you fancy an autumn break in Cornwall.

Meanwhile, back at Canary Wharf in London, there’s a substantial exhibition of Halima Cassell’s sculpture in the lobby of One Canada Square until 30 August. Cassell (born 1975) is rapidly establishing herself as one of the leading innovative cross-media artists of her generation, working in clay, wood, glass, bronze or porcelain. Her distinctive blend of geometric and organic forms articulates a passion for pattern which also says something lasting about human nature.

And, finally, one of the great collage-makers of the 20th century, Robert Motherwell (1915–91), at Bernard Jacobson Gallery, 6 Cork Street, W1, until 30 August, coinciding with a show of his early collages at the Peggy Guggenheim Collection in Venice. Motherwell observed of collage: ‘One cuts and chooses and shifts and pastes, and sometimes tears off and begins again. In any case, shaping and arranging such a relational structure obliterates the need, and often the awareness, of representation. Without reference to likenesses, it possesses feeling because all decisions in regard to it are ultimately made on the grounds of feelings.’ Not a bad explanation of abstraction, and a useful introduction to this entrancing show of beautifully placed and phrased areas of colour and thundering line.