Welcome to Goy Dan.
Depending on the soil and conditions, Look at Pachysandra (Japanese Spurge) Cotoneaster horizontalis, Cotoneaster dammeri 'Bearberry' Ceanothus thyrsiflorus repens 'Creeping Blueblossom', Euonymus fortunei Emerald 'Gaiety' and some Junipers
If you go on line you will also find ground cover collections for sale and Perennial collections start at about £18. Shrubs will cost more.
Finally if you go to Goypeadia there is a page on ground cover plants which shows members photos of these. to find this and other ideas scroll down to the bottom of the page click on G and then select 'ground cover plants'

An important factor in deciding the plants to use is the amount of light the site gets. Is it under trees or facing north, south, east or west? What's your soil like? Sandy, clay, chalky?

I'd echo Volunteer's questions listed above.

It is east facing in an open area that gets a lot of light. The soil is quite fine and holds a lot of water.

Some garden centres do deals on shrubs, something like 4 for £20. In the selection, you'll find things like Ceanothus, Brachyglottis, Hebes, Cotoneasters, so they're pretty cheap, but this time of year is not appropriate for planting Ceanothus and Hebe.
You've said the area is 'roughly 5 or 6 square metres' but haven't said how that's comprised - a long straight border or a square patch or whatever. That would be useful to know - if you knew what you were looking for, sourcing the plants on line from somewhere like Jacksons would probably be the cheapest option (very reasonable prices from them).

The area is a square plot with a wall along the western side.

Oh good, that means you can go for a layered effect, taller stuff to the back, medium in the middle and low at the front. Plants to consider: Large shrubs - Cotinus 'Royal Purple', Buddleia davidii, Cotoneaster 'cornubia', Pyracantha, Viburnum tinus, Berberis darwinii, Physocarpus Dart's Gold, Elaeagnus varieties. Medium - Berberis thunbergii, Choisya ternata, Mahonia aquifolium, Hydrangea, Viburnum davidii, Brachyglottis 'Sunshine' Small shrubs and ground cover: Cistus, Helianthemum, hardy fuchsias such as Madame Cornellisen, Lavender, Hebe Wingletye, Berberis 'Bagatelle', Spiraea Goldmound or Goldflame (bit bigger) Arabis, Iberis, Campanula muralis, Ajuga reptans, Lamium maculatum Beacon Silver or White Nancy.
Note that the Large, Medium and Small refers to height only - some spread out a lot, others not so much, so check the height and spread when you look them up.