What's the furthest distance away from the house and conservatory that you can plant something? This makes a difference to what you can use in terms of root problems.

About thirteen feet think!

You'd be better off with climbers then, as the roots on anything else might be a problem, but for climbers, you'd need fence or trellis supports that were high enough. Only exception would be Cordylines - but they'd take a while to get high enough to be of use as screening. Trachleospermum jasminoides is an evergreen climber with fragrant flowers in summer, if that's any use.

Thank you, we will take your advice.