Exactly - a firm who is not on the list has not got a licence to apply for a Tier 2 or Tier 5 visa and therefore cannot obtain one for you. There is no point in contacting them as they cannot make an exception. If anything you need to find who is on the list, and if they are on the list then ask them whether they apply Tier 2/Tier 5 to graduate roles. Many firms on this list won’t - they will only apply it to senior lawyers or technical business service roles. Some firms despite being on the list, may not meet the individual Tier 2 or Tier 5 criteria for roles.