Oaks don't grow at a fast rate and you almost certainly won't live to see them grow anywhere near to maturity!
They are probably the most wildlife friendly trees, supporting a vast quantity of creatures.
Try sorbus, and hazel along with the beech. Hawthorn is another native that supports wildlife.

The oaks won't act as a screen though once they grow taller you'll see the fence around their trunks. Much better to use hazel, beech and hawthorn as Lut. has suggested all of which can be pruned to keep them at the height you want them to be and will thicken out nicely too.

I assume that you like oak trees so one oak tree in the hedge won't come amis, though they won't make a hedge.

Euonymus europaeus can be bought as bare-root hedging whips and will give pinky-red autumn leaf colour, orange and pink tiny fruits, and is a native, although probably feeds mostly caterpillars. The plants discussed so far have all been deciduous, will this provide enough screening against the fence panels?
For a bit of evergreen, hollies can be bought as hedging whips, and yew should be available too. These may be slow for the first year or two but will then romp away and can be pruned as required. Both are good for small birds to forage in.
If there's room, you could also run native clematis and honeysuckle through them, although I'd maybe give the hedge a year to get its feet down first.
Personally I'd add basic ivy too, but I might be in the minority there...

Thanks everyone. Am excited to plant a lovely selection of (native) plants. I go to 'The Dingle', a lovely nursery in Wales and will be getting a lovely selection of plants. Have just about removed the acidic top layer of evergreen mulch, woodchips and sawdust. 40 bags of the stuff I removed!! Becoming quite a regular at the local dump! It is north west facing so not much sun.

I've just seen your photo. Have a look at a mature oak tree. Wonderful where there's room but honestly I think you haven't unless the fence is a lot longer that it appears in the photo. Think about how wide a mature tree of any kind gets. If its planted near the fence half of it will overhang especially on the South side so if you have neighbours it would cause problems.
Think about the diameter of a mature tree trunk so you must plant some distance from the fence to allow for it, and remember the roots spread out to the same area. Planting trees is planting for the future - you don't want to have to cut it down again before it has a chance to reach maturity. Also you say you love the light you have now the conifers are gone - so do you want to replace them with something that will shade you again when your garden gets little sun anyway? Our garden has mature trees on the East side and even then they cast a lot of shade all morning even though the garden faces south.
I think Teadrinker has good suggestions, though I would be one of those to question the wisdom of ivy, having suffered from it! If you want a wildlife tree why not go for one of the lovely crab apples - they don't get too big and you get both flowers and colourful fruit that the birds love.Stretch a point and get an improved variety rather than the wild one.

Just one tiny point, Oak trees are actually rather quicker growing than people think. They can and do put on 12 inches a year for the first 20 years or so, after that they slow down.

And do you go to the one up above Welshpool or the one at Guilsford?

And a mature oak sheds a lot of leaves. One of my neighbours has two - grrrrr

Owdboggy -I go to the nursery near Welshpool. Great place, good selection of plants and very friendly staff. Point taken about oak tree. Love crabapple and will mix it with a few native like hollies and yew.
Teadrinker - thank you for your wonderful suggestions. Have got some mature Ivy in garden already and don't mind it too much-it offers great screening and have robins nesting in it. It also however provides a home for snails!!!

Have a look at Woodland Trust, they have a lot of info on native trees and planting trees, we planted about 30 for the Millenium, its incredible as Owdboggy says how quickly young trees grow.
you really need to take it into account!

The G/C at Guilsford is the same company/people as the one above Welshpool. There are more herbaceous stuff at the lower one and more trees and shrubs at the mountain side one. We go to both usually. I have to say that they have priced themselves out of my wallet over the last 2 years though, sad really.

Guelder Rose is another hedgerow tree popular around here. ( I think it's a native). It has a pretty light green leaf, white flowers and has clumps of berries which the birds love.

Good suggestion - love them. But make sure you don't get the sterile one that has white "snowball" flowers - no berries on that one.(I did just that...)

I do love the fact that I get my answers without asking a question, I'm following this with interest and now know why I only have snowballs on my new bit of hedging but never get any berries, I guess I need to find another one now, thanks Stera...

Look out for the V.o xanthocarpa form. You get yellow berries which last a bit longer before the birds eat them.

Thanks Owdboggy....

I do sympathise Lincslass - it was very frustrating, and i felt silly when I eventually re read the label - it did actually say it was sterile... I went and got myself the smaller version of opulus that is supposed to grow only to about 5 feet. Hasn't berried yet but fingers crossed.