Most churches in the UK still retain the tabernacle curtain. The curtain/veil goes back to the old Tabernacle or Holy of Holies in the temple in Jerusalem. The veil used in churches therefore gives honour to Our Lord in the Blessed Sacrament by recognising His presence there. It designates the tabernacle as a place of holiness, specifically set apart. And, from a practical stance, denotes to the faithful that the Blessed Sacrament is in the tabernacle (I know we have a lamp too but sometimes they are difficult to see in large churches and easily confused with other lamps).
As far as I am aware every tabernacle should have a white curtain or lining inside, so even if there isn’t one outside there’s one within. *Having taken a quick look at the code of canon law it would appear there’s no directive to have a curtain without or within, only that it be made of suitable, solid, material.