A phone jockey from direct line told me it was... 
It's not illegal, but hey much better to believe a £15k a year muppet, than the guy who runs the whole motor claims piece for one of the largest insurers in the UK.
Reality is that if he tried to explain the true rules behind it then his or your head would explode and / or he'd get it wrong, so here's a basic grounding.
Under the Insurable Interest Act (1774) a person may indemnify themselves against loss of or damage to any of their property.
The concept of indemnity is that you put yourself back in the same financial position as you were before the incident.
When applied to motor policies this mean that you can replace / repair your bike / car once, so you will recieve one payout to place you in the same position.
There is nothing to stop you insuring the vehicle may times over, but if each policy paid out the value of your repairs / vehicle then you would be in a better financial position, thus you would stand to gain from the incident, rather than "stand still". As such multiple policies covering a car / bike for the general public would only be taken out to commit fraud, which is a criminal offence.
So taking out multiple policies is not illegal, claiming on them (for financial gain) is.
There are many rules tha apply and many laws that govern this area, so this is a very basic explanation and there are lots of rules for other disciplines of insurance where multiple policies and multiple claims are legitimate; such as coinsurance, self insurance, marine, disease, liability and the list goes on and on and on.