can you suggest a berry-bearing shrub that would attract birds

Pyracantha springs to mind, though it is a thorny beast. For some reason, the birds seem to prefer the red berried version. Larger cotoneasters, though they do have an arching growth habit, I'm not sure how much room you've got; have a look at Cotoneaster franchetii, or C. frigidus 'Cornubia'.

Amelanchier lamarckii. When the berries appear on this in June, it is full of birds, particularly blackbirds. From a human point of view, lovely bronze tinged new leaves in spring, pretty single white blossom and fabulous autumn leaf colour. One of my favourites.

Normally birds go for red first then orange, black, yellow, white and purple. A native tree/shrub would be best. One that doesnt need much hacking back is best to or else you will chop of the flowers/flowering wood if done at the wrong time.

(B) berries, (S) seeds

Non-native cultivated plants
Berberis species (B)
Cherries, single-flowered species with fruits, e.g. Prunus avium , P. cerasus (B)
Cotoneaster species (B)
Crab and dessert apples, Malus species (B)
Daphne mezereum (B)
Firethorn, Pyracantha species (B)
Holly - female cultivars, Ilex species (B)
Honeysuckle, Lonicera species (B)
Mountain ash and whitebeams, Sorbus species (B)
Oregon grape, Mahonia species (B)
Photinia davidiana (B)
Privet, Ligustrum ovalifolium (B)
Roses, some species with hips, e.g. Rosa rugosa , R. moyesii (B)
Sunflower, Helianthus annuus (S)
Thorns, Crataegus species (B)
Viburnum betulifolium (B)

Native plants
Alder buckthorn, Frangula alnus (B)
Alder, Alnus glutinosa (S)
Birch, Betula pendula (S)
Blackberry, Rubus fruticosus (B)
Devil's bit scabious, Succisa pratensis (S)
Elderberry, Sambucus nigra (B)
Field scabious, Knautia arvensis (S)
Greater knapweed, Centaurea scabiosa (S)
Guelder rose, Viburnum opulus (B)
Hawthorn, Crataegus monogyna (B)
Holly - female plants of Ilex aquifolium (B)
Ivy, Hedera helix (B)
Mountain ash, Sorbus aucuparia (B)
Musk thistle, Carduus nutans (S)
Purging buckthorn, Rhamnus catharticus (B)
Teasel, Dipsacus fullonum (S)
Wayfaring tree, Viburnum lantana (B)
Whitebeam, Sorbus aria (B)
Wild roses, e.g. Rosa canina , R. rubiginosa (B)
Yew, Taxus baccata (B