Holly Blues tend to appear one at a time, and generally fly higher than Common Blues, sometimes re-tracing particular 'circuits' of shrubbery.
The Common Blue is a bit more gregarious. Numbers on an allotment site in Barnehurst - never high - appear to have been very poor last year, though I wasn't around so much.
On the day of the mating pictured below, three were seen at once on the most favourable plot, flying about randomly at about 4' off the ground. The favoured nectaring plant was Geranium pyrenaicum (white-flowered form).
A few days later I had this female in my garden, pictured at rest on the purple-leaved cultivar of culinary Sage.
If Common Blue caterpillars do develop in this area, Black Medick is likely to be the main foodplant.