Working holiday - One year insurance

I'm planning to go on my working holiday for a year (From the UK) and the embassy's website advises getting insurance first. It's proving difficult to find cover for a one year long trip rather than annual multi-trip insurance. I've seen prices from £200 up to £500.
What's the cheapest place to get it from? I'm on a budget.
It's recommended by the embassy in case of accidents, but would I run into a problem if I didn't get any? (Assuming I spent my year with no health problems and accidents!)

What you can get from the UK would be traveler's insurance. I didn't know that they advised working holidaymakers to get insurance "first."

Once you are in Japan, and you know that you will be here for one year, then you will need to sign up with the Japanese National Health Insurance scheme.

(Assuming I spent my year with no health problems and accidents!)

That's a big assumption (otherwise, nobody would ever buy insurance!).

Also, remember that your own health is not all you have to worry about. You need insurance also to cover you in case you accidentally cause damage or injury.

It does sound like a big assumption, but I've managed to make it to 27 years without incident, so I figured I might be fortunate one more year!
That aside, from the UK embassy of Japan's site:
"It is recommended that insurance coverage be arranged before leaving the United Kingdom, as under the conditions of employment for the Working Holiday Visa the period of employment is usually not long enough to qualify for coverage provided by employers or companies."

I've read about some people joining the Japanese national health insurance, but also someone else WASN'T able to join (Perhaps they were from another country and it was a while ago, too.)

So like I've read, they'll ask me to join the JNHI when I visit the government office to get a resident registration?