fast growing hedging

Escallonia would be my choice, it is evergreen, fast growing and has flowers, white, red or pink. It is easy to maintain and can be trimmed, it is also pretty easy to get hold of and inexpensive.
There is of course laurel, but that can get huge, but has large glossy leaves and is pretty fast.
Have a look on the internet under evergreen hedge. It should give you information on upkeep and growth, you will have plenty to choose from

I like Choisya ternata, for its white fragrant flowers at least twice a year, and its pretty leaves. That can be cut back, too.

You may find Laurel best for you. If you want a 6ft. hedge now is the time for you to plant them.
Large bushes will soon form a dense hedge. 22ft. would need 7 bushes, which should fill the gap.

Some bamboos are fast growing, all are evergreen, and they make lovely rustling noises in the wind. Expensive tho' for a long hedge - maybe £10 ish per foot.

my favorite is grisellinia. it keeps all its leaves all winter. only little flowers but its a lovely bright green all year. only needs trimming once a year.

how about Photinia? P. x fraseri 'Red Robin'. would be my choice and will get to approx 8ft. or if you want it to get taller, go for P. fraseri 'Robusta' both are good all rounders, evergreen, flowers late spring/early summer, and the new growth is bright red.

Holly is great. How about a mixed native hedge? You could grow holly, yew, hawthorn. I have one and it is very nice, good for wildlife and interesting all year round.

Native hedges are the best option, but things like yew are really slow growers and very expensive. My brother has just had the difficult task of trimming a holly hedge, not a task he found very enjoyable.................

Both Beech and Hornbeam tend to keep their dead leaves through winter and are quick growers and very cheap.

The Escallonias can't be beat for your requirements (IMO). Forget any bamboo for your needs. 'Red Robin' is slow to start and then becomes a large brute though it's attractive, ditto for laurel. But to return to the escallonias. Be careful which you choose. I've found E. greenii to be an excellent hedge in the same situation as you require and I hack the top every April to ensure my chosen height. Greenii is also a plain green which makes an excellent foil and background to a border. Then there are many excellent varied forms to choose from. Remember too that escies are evergreen unlike Beech and Hornbeam.

And another thing, 22ft of mature hedge in years to come can make for a lot of clearing up each year! Can you get rid of it?

I'd avoid holly as it is far too slow growing.
I think it would also take choisya several years to reach a height of 6 feet