Is it a fence? Trellis can be good then a range of climbers

Have the leylandii gone or are the roots still there?

Eucalyptus grows fast and is every green as is Loquat, Laural and the like. Birch and Rowan also grow fast but are not evergreens so are a poor screen. Bamboo make a good screen.

All the leylandii have now gone for good, thankfully, and we have fencing but the other problem is that we have two dogs so didn't want anything with berries

Your soil may need improving after the leylandii.

have you looked at the alphabet at the bottom of the page?
Choose S and then screening ideas, you can see members ways of tackling the problem and ask them questions if nessesary.
I could think of some ideas but have a look there and ask more questions if you wish either by answering below here or my a complete new question, lots of our members have dogs.....check out the photos and blogs :0)

Leylandii roots do not grow again when cut down.
It depends if you want evergreen trees, to provide colour
in the winter.
Take your time over this. Follow advice of Pamg.

Remembered I did have 3 Thujas that grew about 8 feet in 5 years. Were not expensive.
Left them on my allotment which I left because of vandalism.
Told they dont exceed 12 feet. Dont need pruning, dont make any work.
Worth checking up on.

Thuja's much better than the dreaded leylandii .....but I like it all.....flowers and evergreenery :0)

Thank you for your advice its much appreciated xx