The other answers explained why it would not help you to have overlapping coverage for property with multiple insurers.
With health - the insurance pays for a treatment, and you can't usually have the same condition treated multiple times, so if your insurance covers it - it will pay. You can still have multiple policies (although in UK there may be legal limitation since the government essentially is the insurer). Consider you have one policy that only covers emergencies, and another that only covers illness during travel. If you have a heart attack during travel - both will cover it, but the hospital where you'd be treated will ask for someone to pay, and will bill that one. You'll have to chose which of them to charge (or, as others have mentioned, the insurers will split the costs between them).
With life, however, there's a difference. You can have multiple life insurance policies, and you may get into a situation when you lose your life in an event covered by all of them. Unless explicitly stated otherwise in the policy, they will all pay. This allows you having multiple policies for different beneficiaries and different amounts.
For example, assuming you're a husband and a father, you can have one policy with proceeds going to the kids, another with proceeds going to the kids of the mistress, and the third one split evenly between the wife and the mistress, having them scratch each others' eyes out while dealing with the insurer because you actually hated them both, and have a fourth one for the guy you were actually in love with your whole life but didn't want anyone to know because your family would banish you. They will all pay, and they won't talk to each other or let the beneficiaries of the other policies know.
The reason for the difference is simple: you cannot put a price tag on one's life, thus you can never over-insure it.