Does the planting area get at least 6 hours of sun per day? Most of my recommendations require lots of sunshine.

Yes Bathgate, in as far as we get Sun, the site is south facing and catches any Sun there is.

I've got some lovely blue and pink perennial geraniums which need very little looking after. Can't tell all their names but one of the blues is Johnsons Blue.

Six inches wide isn't very big - if anything you plant there is allowed to cascade or lay over the edge of the patio, then that allows for better planting, but if there's a lawn the other side, whatever you plant may well sprawl over that too. Perennial Geraniums such as 'Wargrave's Pink' do get sprawly, and they disappear in winter - if the area is very sunny, and you can allow the plant to sprawl over the patio without it interfering with the lawn, then something like Helianthemum (Ben Mhor or Ben Fada for instance) would do nicely - these are evergreen. They flower around May time.
Alternatively, Ophiopogen nigrescens, commonly known as Black Grass, is also evergreen and produces little pink flowers in late spring/early summer, but is primarily grown for its leaf colour. Also not at all sprawly, so may fit well in a border that size. You could mix it with Liriope ariaki-jenshigi, a yellow and green striped Lily turf which produces fairly short stemmed purple flowers in late summer/autumn, again, evergreen.

Geraniums don't need lifting - they're hardy herbaceous perennials (so I imagine you're talking about Pelargoniums...?). And geraniums sprawl, so a 6" border won't be wide enough unless you don't mind that. Also, although there are geranium varieties which are evergreen, many are not, including G. 'Johnson's Blue' which dies down in autumn and doesn't reappear till spring.

It's hard to advise you without knowing what sort of an effect you're after and what sort of soil you have, so some detailed info would be useful.

Bamboo's suggestions are great. Even Helianthemums tend to get a bit wider than 6" though - if you could double that you'd have a much better chance of it looking good. I've never come across a perennial geranium that would stay as small as that.

Hard to visualise just what you've done - is it lawn on the other side of the new trench? If it is you'll have your work cut out to keep it from growing into the bare area. If its hard standing of some sort you might consider something like creeping thyme, when it wouldn't matter if it did spill over.

Or Erodium 'Bishop's Form', that flowers from late spring through to autumn... but does spread out widely. best in milder areas or a very sheltered spot though - links below

Ophiopogon:
https://www.rhs.org.uk/plants/details?plantid=3636

Liriope variegata (you probably won't find the ariake one I mentioned):
http://www.jacksonsnurseries.co.uk/liriope-muscari-variegata.html

And Erodium:
http://www.plantsforsmallgardens.co.uk/erodium-x-variabile-'bishop's-form'~136

Thank you all folks, will be following up on your helpful suggestions. Happy gardening