These are policies that pay out either if the person insured contracts one of a range of critical illnesses, or upon death, but not both.
Instead of taking out separate cover so that they are protected in either event, families may have to choose whether to accept money from their policies straight away.
Doing so - and helping to alleviate the effects of diseases such as cancer, heart attacks or strokes - will leave the family with nothing should the policyholder die.
The problem arises because most critical-illness insurance, relatively unknown until a few years ago, has been sold on an 'accelerated' basis as a promotional exercise. In effect, insurance companies pay policy- holders upon diagnosis of a critical illness rather than compensating the estate at death.
Every year almost 500,000 people suffer heart attacks, strokes, or contract cancer for the first time. More than half will live for at least a year, with increasing numbers surviving far longer. Last year, about 230,000 critical-illness policies were sold in Britain, about 30 per cent more than in 1992.
But numbers of free-standing policies bought rose by 63 per cent in one year alone, suggesting that up to now not everyone has bought fully appropriate cover.
Tony Solomon, protection manager at Eagle Star, said: 'Accelerated policies can be a good thing. But there is a great need for stand-alone cover. People should not have to choose whether they get money now or at death. The problem is that many companies have sold the concept as a cheap bolt-on option to life cover.'
Eagle Star has a separate critical-illness product which, under its Rainbow plan, can be combined with life cover. For pounds 20 a month, a male policy- holder aged 30 will get critical- illness cover of pounds 54,000. His family will receive an equal amount on his death.
Sun Alliance last week launched a Universal Protection Plan. For pounds 10.44 a month, a person aged 30 receives pounds 50,000 on diagnosis of critical illness. Death benefits worth pounds 20,000 are also payable.
Norwich Union last week launched a policy that covers people in the event they contract rheumatoid arthritis.
John Joseph, a London consultant specialising in critical illness, said: 'Of course, if a person has a family and can afford both critical-illness and life cover, rather than accelerated policies, it always makes sense to have both.
'But for many people that is not an option. Besides, the whole point of critical illness is that it is like an airbag in a car. You only realise you always needed it a millisecond after the car has crashed.'
One person grateful for having had critical-illness cover is Susan Hill, of Kettering, Northants, who runs her own training consultancy.
Mrs Hill, 39, and her husband Bernard were persuaded about three years ago by Allied Dunbar, their consultant, to have a stand-alone policy each, plus another linked to their mortgage. Two years ago Mrs Hill had a massive stroke.
She said: 'I was in the kitchen. I had been gardening all morning, when I felt a blinding pain in my head.'
For the next few months Mrs Hill was moved between hospitals in Kettering, Oxford and, when she needed further rehabilitation, in Cambridge.
A few days after she was taken to hospital, however, her Allied Dunbar consultant visited Mrs Hill with a cheque for pounds 175,000, the proceeds of her critical-illness policies. The money enabled her husband to give up his own job for a time to assist with Mrs Hill's recovery.
Allied Dunbar is deferring the premiums on her personal pension plan until she recovers. She also has separate life cover, so that if anything else should happen her family will be protected further.
Mrs Hill still has some weakness in her left side and walks with the aid of a stick. But she said: 'I'm hopeful of returning to work and I do not intend to let this grind me down. Most of all, I'm grateful that I took the consultant's advice. This has made things much easier than they would have been.'
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