We present a catalogue of ~3000 submillimetre sources detected ( greater than or equal to 3.5...) at 850 ...m over ~5 deg super( 2) surveyed as part of the James Clerk Maxwell Telescope (JCMT) SCUBA-2 Cosmology Legacy Survey (S2CLS). This is the largest survey of its kind at 850 ...m, increasing the sample size of 850 ...m selected submillimetre galaxies by an order of magnitude. The wide 850 ...m survey component of S2CLS covers the extragalactic fields: UKIDSS-UDS, COSMOS, Akari-NEP, Extended Groth Strip, Lockman Hole North, SSA22 and GOODS-North. The average 1... depth of S2CLS is 1.2 mJy beam super( -1), approaching the SCUBA-2 850 ...m confusion limit, which we determine to be ... 0.8 mJy beam super( -1). We measure the 850 ...m number counts, reducing the Poisson errors on the differential counts to approximately 4 per cent at S sub( 850) ... 3 mJy. With several independent fields, we investigate field-to-field variance, finding that the number counts on 0.5...-1... scales are generally within 50 per cent of the S2CLS mean for S sub( 850) > 3 mJy, with scatter consistent with the Poisson and estimated cosmic variance uncertainties, although there is a marginal (2...) density enhancement in GOODS-North. The observed counts are in reasonable agreement with recent phenomenological and semi-analytic models, although determining the shape of the faint-end slope (S sub( 850) < 3 mJy) remains a key test. The large solid angle of S2CLS allows us to measure the bright-end counts: at S sub( 850) > 10 mJy there are approximately 10 sources per square degree, and we detect the distinctive up-turn in the number counts indicative of the detection of local sources of 850 ...m emission, and strongly lensed high-redshift galaxies. All calibrated maps and the catalogue are made publicly available. (ProQuest: ... denotes formulae/symbols omitted.)