Check with your council on the permitted height for hedging next to the roadside.
You cannot plant a fully formed hedge, most hedging plants ( apart from leylandii which you should steer clear of) may take years to provide the privacy you have with your wall and fence.
Hedging is expensive, much more so than fencing. I planted a hedge 2 years ago and you can still see through it, though its also got post and rail fencing behind it. I used this company:
https://www.hedgesdirect.co.uk/