'Deep Cleaning'
It should be noted that if the above advice has been followed then 'deep cleaning' should not be necessary. 'Deep cleaning' should be seen as a last option after trying the above cleaning advice, repeatedly using these methods will alter the appearance of the sink and reduce its lifespan. You should start with the (first) least aggressive method.
1. Absorb as much contaminate as possible with kitchen roll, rinse with lots of hot water.
2. A proprietary kitchen cleaner and a stiff nylon brush with less than 5% bleach content.
3. 'Bar keepers friend' or 'Cif' cleaning cream and a stiff nylon brush or nylon scrubbing pad, this is good for removing stubborn stains and silver marks from metal cookware.
You should always rinse the sink thoroughly after following any of the above steps, it is worth noting that stronger chemicals should not damage the sink itself but would damage the waste kit so should be avoided.