Posted: 25/03/2014 at 16:45
Patience. As a start I would carefully remove all the ivy from these trees to ground level and treat the cut stumps with a strongish mix of glyphosate or other suitable treatment. Be careful not to damage the tree bark with your tools or the ladder.
Next winter you will be able to see the shapes of the trees and start to cut out dead, crossing, weak or misshapen branches. But don't try to do much shaping per year or the trees will throw out loads of water shoots. You will probably have decided by winter which trees you want to keep (what varieties do you have?) and which others are not really worth the space they're taking up. Then you can look at planting some new trees which will crop much better and you won't have trouble picking them.
In the meantime, I'm sure you've got lots of other jobs in your new garden - you seem to have a lot of leylandii!