Privet?

common laurel?

or for something much prettier photinia red robin

My choices would be:

Photinia

Thuja

Bamboo

Bear in mind that the quickest to grow will need most maintenance.

conifers [fast growing] Portuguese laurel or bamboos.The bamboos already have instant height and will then both grow taller AND thicken out.

Photinia whilst being visually good to look at will be expensive if purchased as large subjects. Bamboo will be untidy and will take a beating from cold winds and winter weather and the roots will become invasive. Thuja will do a good job as it will be quick growing and responds to trimming. My vote would go to the Portuguese laurel (Prunus lusitanica), slender leaves and purple stems, although vigorous will not end up being the beast as with the common laurel (Prunus laurocerasus Rotundifolia).