The Australian-English phrase like a beaten favourite is used to denote physical ugliness.
—Synonym: like a twisted sandshoe.
—Cf. also like a robber’s dog.

I have, however, found a British-English occurrence of the phrase like a beaten favourite used in a different sense in the following from Liverpool are just champion, by Hugh McIlvanney, reporting from Anfield, Liverpool Football Club’s home ground, published in The Observer (London, England) of Sunday 16^th May 1982:

Liverpool, who were placed twelfth in the First Division last Christmas and labouring like a beaten favourite, came through comfortably yesterday to take their fifth Championship in seven seasons.

The earliest occurrences of the Australian-English phrase like a beaten favourite that I have found are as follows, in chronological order:

1-: From the review of Four Lady Bowlers in a Golden Holden, a revue by the Australian author John McKellar (1930-2010)—review by Leo Schofield, published in The Sydney Morning Herald (Sydney, New South Wales, Australia) of Saturday 27^th November 1982:

When he captures the real Australia in expressions like “She’s got a head like a beaten favourite,” McKellar is at his timeless best.

2-: From Mongrel B*st*rds, by a pseudonymous Dr Sir Leslie Colin Patterson, “cultural attaché to the Court of St James’s from 1975 to 1998”, published in The Spectator (London, England) of Saturday 1^st April 2000:

Naturally I was pretty nervous before I hit Old London Town the first time, wondering how I was going to spend the arduous years as cultural attaché to the Court of St James’s with the back of my hand-stitched, powder-blue, Crimplene safari suit permanently pressed to the wall. At Heathrow aerodrome I had my first taste of English hospitality, standing at the end of a long queue of Aussies and Kiwis whose uncles had more than likely stopped a bullet in defence of the Pommy Empire, while all those tea towels and bush-bunnies flashed past in the fast lane through immigration.
There was a waiting limo laid on for me by my old friend the Australian taxpayer and there I met my driver Terry, a typical whingeing Pom with a face like a beaten favourite.

3-: From tv previews, by Henry Everingham, published in The Sydney Morning Herald (Sydney, New South Wales, Australia) of Monday 12^th March 2001:

Something in the Air
ABC, 7.30 pm
If you don’t give two hoots, have a head like a beaten favourite, know how to put a rocket up ’em, or simply pine for A Country Practice, Emu Springs may be just the place for you tonight.
Wayne Taylor has just finished a two-year lagging for nicking a car, but he isn’t exactly being made to feel welcome back in this rural backwater. Why the deluded sod would ever return to somewhere so dull is beyond anyone’s comprehension.