Astronomers say that the prime moment to see the light show will be between midnight and dawn on November 17-18 as long as the weather is settled.
Although they can be seen with the naked eye, they are best viewed with clear skies away from light pollution.
Those who miss the peak on Wednesday night might still be able to view the shower through the week, as it continues at a reduced rate for several days on either side.
Meteors - also known as 'shooting stars'- are typically either bits of asteroids leftover from the formation of the solar system or, as in the case of the Leonids, material ejected from the disintegration of a comet as it passes near the Sun.
These beautiful streaks of light seen in the night sky can be caused by cosmic particles that are as small as a grain of sand.
The Met Office forecast for Wednesday to Friday is for changeable weather in the north with spells of rain or showers and often windy.
Talking about this evening's weather (November 17), a spokesman for the Met Office said: "A few clear spells during the evening, but cloud amounts increasing from the west, with outbreaks of rain and drizzle developing in many areas.
"Remaining mild, but windy. Minimum temperature 7C."
Displays are better when the Tempel-Tuttle comet, which takes 33 years to orbit the sun, is closer to the Earth, an occurrence which is next due in about 15 years' time.
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