So I turned off the water at the mains, removed the tap and replaced the worn washers. I thought that this would be the end of the story but when I turned the water back on at the mains the drip was still there!
I decided to go online and see what else could be causing the problem and found out that my tap might need reseating. This is when calcium and corrosion build up in the tap and prevent it from closing off tightly.
I found the links below very helpful in guiding me on what I should do and soon the leaky tap was fixed!
UltimateHandyman YouTube Video: Tap reseating