Hi,
There really are so many variables to this but I will try and simplify it so you have an idea what to look out for.
Check your existing cover for sickness where you work, this will determine your deferred period.
Short term cover with back to day 1 payments would be more cost effective with a stand alone Accident, Sickness, Unemployment policy (ASU) About 5.00 per 100.00 cover, this policy would cover your mortgage payments and allow 25% extra cover so long as it does not take the benefit to more than 75% of your income. Any claim can last no longer than 12 months usually.
Longer term protection of income would be provided by Permanent Health Insurance (PHI) this is longer term cover up to 65 years of age, but only covers sickness and disability. Will allow benefit of up to 75% of income and is usually index linked. This policy is more expensive but can be cheaper with a longer deferment period.
E.g. ASU policy back to day 1, accompanied by PHI with a 52 week deferment would cover you in the short term for all aspects of loss of work with the benefit of long term benefit through a long illness.
Critical illness is a one off payment usually for the benefit amount on diagnosis of specific conditions. Can either be used to pay mortgage off or provide long term care costs.
These are basic examples and descriptions. You should seek professional advice and I hope that this post gives a clearer picture.
Regards Ian