Hi taniaw67
New Style ESA is a Contribution Based benefit and is not means tested with the exception of pension income which can reduce the amount that you receive.
The Income Related benefit that goes with NS ESA is Universal Credit.
From your post you state that you are on CB ESA and IR ESA these are what we call legacy benefits which are no longer open to new claimants.
You ask why in UC why does contributory amount get removed, the contributory amount in UC is called New Style ESA, this is a contribution based benefit, you can also apply for UC at the same time as NS ESA, but the NS ESA will be deducted £ for £ from your UC claim.
You may need to seek advice from your local Welfare Rights Organisation; you can find your local Welfare Rights Organisation to help you with advice by clicking on the link below and putting in your post code, it will then come up with a MAP with a list of agencies.
advicelocal.uk Gary