One slightly upsetting aspect is not with sharia at all, but with British civil law -
...the British courts do not recognise Islamic ceremonies carried out in this country unless they are registered separately with the civil authorities. The result is that some Muslims think they are protected by family law when they are not, and others think they are properly divorced when, in fact, they are still married. In one case, Luton police contacted WLUML [Women Living Under Muslim Laws] after pursuing a man for bigamy who had married in Luton, then flown to Pakistan and married again. After looking into the case, they found that the first marriage was invalid as it had been conducted by an imam in an unregistered mosque. His first wife was left with no legal protection by the family courts, and the husband was free to bring his second wife back to Britain as his legal spouse.
In Australia, the first wife would be protected by the fact that she had been living in a "marriage-like relationship". She would be able to leave the marriage and claim her property and child maintenance. I can't believe that in the early 21st century, Britain doesn't recognise common-law marriage!