Photinia red robin does get rather large, and you'll need to be keeping it in check 2 or 3 times a year (once its got going) in your situation. I'd be more inclined to choose something like Berberis darwinii, which only gets 8 feet at maturity rather than the 20 x 12 feet or more that Photinia wants to reach. Berberis are prickly though, and you may not like that too much when having to trim it, but it won't need trimming so often as Photinia and has much smaller leaves, more suitable for a small space. Orangey yellow flowers usually in May, and you prune back after those, maybe again in September just to keep it tidy, once its established.

For a shorter hedge, Lonicera nitida 'Baggesens' Gold' or 'Lemon Beauty' - evergreen, small leaved, will make about a metre to 1.5 metres in height, tolerates shade well.

Not sure where you are in the UK, but if its somewhere built up like London, Cotoneaster simonsii is worth considering - its listed as semi evergreen, like all the cotoneasters, but in milder areas is likely to retain its leaves all year.

Thank you so much for this suggestion. I have had a look on the rhs website, and the only thing putting me off Berberis darwinii, is that it says it will take 10-20 years to reach the full height of 1.5-2.5 metres. I am a bit worried that I won't achieve my aim of getting any privacy for a very long time!

I am Shropshire/Welsh borders area, so does get very cold!

The trouble with more rapid growing varieties is, they don't stop growing, so over time, they're a lot more work year on year. And I don't agree with that time scale at all - I've grown this shrub a lot in various gardens - if the plant is already a foot high when planted, it'll be around 4 feet after 3 years, specially if you dig the soil over and add plenty of composted animal manure first, prior to planting. Even the Photinia you're considering won't be 6 feet for 4/5 years. If you wanted a quick privacy screen, might be wise to invest in some of that roll out bamboo stuff, attach it to a few upright bits of wood, and remove it once whatever you've planted is high enough, assuming it won't exclude to much light... Or, dread the thought, stick up some nets in the window and get rid of them later...

You can buy 'instant hedging' if you've got lots of money - this is a hedge that's already 4 or 5 feet high, transported and planted direct in your own soil, but it is very expensive and needs extra care so it doesn't die - mature plants don't adapt to new conditions so readily as young ones do.

I did think that 10-20 years sounded like a very long time! But, growing it to around 4 feet over a period of three years seems realistic and I would happy with that.

I wonder if the rhs website over estimates the time scales for similar shrubs, as it appears that a lot of these medium sized shrubs take a very long time to reach their full height.

Again, many thanks for all your help, its very much appreciated!

Well, they're probably compensating, if what you looked at was regarding hedging plants specifically - when you grow hedging, it needs to be pruned down, usually in the first year, and often again in the second year, to encourage branching at the base so you don't have big gaps at the bottom.

Oh Ok, that does makes sense. I had no idea that had to be done. I have learnt a lot on here - thanks again :)

There's probably instructions regarding that for particular hedges online - maybe even the RHS.

Do you mean privacy to stop people looking in to your front room or privacy to mark the change from public footpath to private garden?

If the first then try net curtains or Venetian blinds.
If the second, have you considered iron railings or a fence - that way you don't lose any of the space in your garden and you don't have the constant battle against an overgrown hedge.