I am working in a hospital in U.K and sometimes serve food for the patients, Am I allowed to give the patients pork or ham?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
Muslims are not allowed to serve any meal that contains pork nor to help in carrying it or doing any other kind of help. This rule is the same whether it is served to Muslims or non-Muslims, as doing such a thing is helping them in sin and transgression.
Allah Says (interpretation of meaning): {but do not help one another in sin and transgression.}[5: 2].
So, one should avoid serving any forbidden things, pork, alcohol, dead animal meat, etc.

Allah knows best.