Posted: 30/07/2016 at 16:30
You'll need to remove the stumps and put plenty of goodness back into the soil which will have been severely depleted by the leylandii. That'll be quite a project in itself and needs doing before you plant anything new be it young bare root whips or mature specimens.
Fairygirl is right about mature specimens. They'll cost a fortune and take years of TLC to establish and grow away. I suggest you have a look at plants like hawthorn or beech or hornbeam which can be planted as bare root whips in autumn. You then cut them back to about 9" and water in well.
We did this with hawthorn and it grew 6' the next year. We then cut it back by half to make it shoot sideways and thicken up. It's great for wildlife too. Copper beech will keep its dry leaves over winter and give extra privacy if you need it. The old leaves finally fall as the new leaves start to shoot in spring. Hornbeam is better for damper soils. All 3 can be kept clipped to make a neat, dense hedge.
Evergreens won't grow as fast but you could also consider pyracantha which has spring blossom and berries to attract a wide range of wildlife plus thorns to deter intruders. Laurel is very dark and dull and looks awful if clipped with hedge trimmers as it has large leaves whose edges go brown when cut. Photinia Red Robin makes a good hedge and has fresh red growth in spring and when it's been trimmed.