What are the minimum and maximum monthly premiums for Critical Illness cover?

Minimum premiums vary from company to company depending on their own policies, but they could be as small an amount as £5 per month.
When it comes to the maximum premium it is hard to say as it all depends on how much cover you require, your age and health, and what optional extras you have chosen.

Your main consideration should be to make sure that you are covered sufficiently so that if you become seriously ill you receive a large enough payout to enable you to maintain your lifestyle, and ideally pay off any outstanding debts like a mortgage. Don't compromise on your sum insured unless you really cannot afford the monthly premiums.

If you decide that you want to increase your cover and therefore your premiums at any point, you may be able to do this. Check that the insurance company offers this flexibility before signing up to a policy.