See figure 1.3a - https://www.gov.uk/government/publications/migration-advisor...
Note that to the best of my knowledge, these numbers don't include the Afghan resettlement scheme which would further lower the proportion of employment driven visas.
Who indeed will pick the cotton.
The sorts of "progressives" who unconditionally support mass immigration are just useful idiots being used as tools by said elites to enforce their narrative. Just have to push the idea that "disagreeing with this is racist" and they'll all support it without question.