Sounds like you need income protection insurance more than life insurance.
This.
I have both life insurance and income protection insurance but both are for different reasons. The life insurance is there purely to pay off the mortgage (and some left over) so that if I did my Wife doesn't have to worry about paying the mortgage or really worry about money again. It gives me absolutely no benefit and if I had no wife / family I wouldn't bother and the bank could just take the house back to pay off the debt.
Income protection on the other hand is awesome, you need to design it to match your sick pay from work (which could be difficult in your circumstances). Essentially work out how long you could afford to support yourself without pay and that's the deferral period before income protection would kick in. The longer you can set this the cheaper your policies will be, significantly so in some cases. For example I get 6 months full sick pay and 6 months half so I actually have two policies that stack together. One of them kicks in after 6 months but only pays a small amount, the other one kicks in after 12 months and pays significantly more. When the two stack it covers about 70% of my normal salary and is a guaranteed index linked payment that runs all the way up until I hit 60, or can return to work.
There are a few "must haves" you need to look for with Income protection. It needs to be index linked or in 30 years your payments could be worth a fraction of what they are now, you also want it to have an "own occupation" clause. They normally come in three kinds, any occupation, similar occupation, or own occupation. Essentially it boils down to what work you could do. If you were a 6 figure earning business CEO with a "any occupation" clause and something stopped you running your business for health reasons but you could stack shelves in the supermarket you would loose your insurance if you didn't take that job. If you have the own occupation clause you don't have to go back to work until you can go back to a job of the same caliber as your own. You also want it to be a guaranteed policy. This means that other than inflation your payments never go up. This is particularly excellent if you start it when you are young.
Although most people cover this with "critical illness" tagged on to the life insurance if you actually read the details on this some of them are incredibly specific on what circumstances have to occur for you to get your payouts. Income protection is much simpler in that if you are too sick to do your job, you get the payment.
The only bit I wouldn't have is the unemployment cover (They normally come as Accident / Sickness, or Accident / Sickness / Unemployment). My reasoning for this is that this is really there to protect against very long term sickness / health issues and not a short redundancy. When I did quotes for my circumstances covering unemployment the quotes were well over double.
In short, income protection is awesome and everyone should have it!