In grappling with the problem of catastrophic illness, the House of Representatives has come up with a cure that may be worse than the disease. The plan approved on July 22 by a vote of 302 to 127 would take us a giant step toward national health insurance in the British fashion. This fatal journey ought to be resisted.

Beyond dispute, the problem of a catastrophic illness is indeed a problem, and a devastating, heart-wrenching problem at that. Any family that has experienced a prolonged hospitalization, with accompanying expenses for nursing care and drugs, knows the meaning of ''catastrophe.'' Such illnesses can wipe out savings, destroy family relationships and reduce the most prudent families to penury. President Reagan acknowledged this last year, when he asked his secretary of health and human services to make recommendations.

One trouble with the House bill is that it goes miles beyond what Secretary Otis R. Bowen proposed last November. The secretary's plan contained some of the same drawbacks of the House plan, but it was relatively moderate in both its benefits and its cost. The House bill would hit the elderly with mandatory fees that could prove a real hardship for many persons now on Medicare.

Under the House plan, Medicare patients would be entitled to unlimited free hospital care after an initial annual deductible of $580 in 1988. The bill guarantees that no Medicare patient would pay more than $1,043 out of pocket for covered doctor and outpatient bills. The plan would pay 80 percent of a patient's prescription drug costs above $500 a year. It would cover 150 days in a skilled nursing home after an initial charge of $168.

For a patient with high drug costs, the total out-of-pocket cost to a beneficiary would be capped at about $2,300 annually, plus 20 percent of drug costs exceeding $500. At present there is no limit on out-of-pocket payments, and hospital stays are covered (after a deductible) for only 60 days. The bill justifies Rep. Dan Rostenkowski's description. The Illinois Democrat termed it ''the most significant and far-reaching expansion of Medicare'' since the program was created 22 years ago.

The estimated cost of all this is $34 billion over the next five years, almost double the $18 billion price tag on a more restrained Republican proposal. The House plan would be financed by increases in the monthly premium for Medicare. That premium now amounts to $215 a year. It would go to $378 a year in 1992.

Two basic objections may be raised to this legislation. It invites political sweeteners in years to come, and it would just about destroy any incentive for the private insurance carriers to offer coverage to the elderly.

If the House bill becomes law, it would be only a matter of time -- and not a very long time -- before political considerations would lead to beefing up the benefits. It would be marvelously easy, and marvelously appealing, to reduce the $580 deductible to $400, to $200 or to nothing at all. Instead of paying 80 percent of drug costs above $500 a year, why not woo the voters by covering 100 percent of drug costs above $100 a year? Mr. Speaker! Can't we do more for the old folks?

This way lies national health insurance, with its monstrous costs and its terrible damage to the whole system of private health care and private health insurance. A greater blunder in public policy scarcely could be imagined.

There are alternatives to going the government route. The House plan is inflexible: specific benefits, specific costs. By contrast, private insurance carriers, competing for the elderly market, are in a position to offer flexible plans tailored to individual purses. Vouchers could be provided through Medicare, by which retirees could purchase such policies. Congress could require employers providing tax-deductible health plans to provide catastrophic protection also. The states ought to be encouraged to experiment with risk pools to protect uninsured families.

My thought is that not enough creative thought has yet been applied to tackling the problem. Such liberal Democrats as Pete Stark of California, principal sponsor of the bill, tend to think first of solution by government -- tax and tax, spend and spend, and leave it to Uncle Sam. I'm not suggesting there is no role at all for Medicare. Probably there is. But recourse to the federal monolith should be the last resort and not the first.