If an insurer asks for a higher premium because I am 'Rated', is it worth applying to another insurance company?

The underwriting standards are very similar between insurance companies because they are all adhering to the same industry standards. If one insurance company Rates you, they all will.
You will probably apply for life insurance with the company that offered you the cheapest initial quotation. So if you apply to the second cheapest insurer and they Rate you too, the rating will still be even more expensive than the first.
Your age is one of the most important aspects relating to your premium, and most insurance companies work out your age in quarter years. Each quarter year is more expensive than the last. If you need to take a medical for one company then you will need to take a medical for the next company. Meanwhile time is passing you and your Application may well move your age into the next older quarter. This means an automatic increase in your premium even before you've been Rated!