Context. Model atmosphere analyses have been previously undertaken for both Galactic and extragalactic B-type supergiants. By contrast, little attention has been given to a comparison of the properties of single supergiants and those that are members of multiple systems. Aims: Atmospheric parameters and nitrogen abundances have been estimated for all the B-type supergiants identified in the VLT-FLAMES Tarantula survey. These include both single targets and binary candidates. The results have been analysed to investigate the role of binarity in the evolutionary history of supergiants. Methods: tlusty non-local thermodynamic equilibrium (LTE) model atmosphere calculations have been used to determine atmospheric parameters and nitrogen abundances for 34 single and 18 binary supergiants. Effective temperatures were deduced using the silicon balance technique, complemented by the helium ionisation in the hotter spectra. Surface gravities were estimated using Balmer line profiles and microturbulent velocities deduced using the silicon spectrum. Nitrogen abundances or upper limits were estimated from the N ii spectrum. The effects of a flux contribution from an unseen secondary were considered for the binary sample. Results: We present the first systematic study of the incidence of binarity for a sample of B-type supergiants across the theoretical terminal age main sequence (TAMS). To account for the distribution of effective temperatures of the B-type supergiants it may be necessary to extend the TAMS to lower temperatures. This is also consistent with the derived distribution of mass discrepancies, projected rotational velocities and nitrogen abundances, provided that stars cooler than this temperature are post-red supergiant objects. For all the supergiants in the Tarantula and in a previous FLAMES survey, the majority have small projected rotational velocities. The distribution peaks at about 50 km s-1 with 65% in the range 30 km s-1 ≤ vesini ≤ 60 km s-1. About ten per cent have larger vesini (≥100 km s-1), but surprisingly these show little or no nitrogen enhancement. All the cooler supergiants have low projected rotational velocities of ≤70 km s-1and high nitrogen abundance estimates, implying that either bi-stability braking or evolution on a blue loop may be important. Additionally, there is a lack of cooler binaries, possibly reflecting the small sample sizes. Single-star evolutionary models, which include rotation, can account for all of the nitrogen enhancement in both the single and binary samples. The detailed distribution of nitrogen abundances in the single and binary samples may be different, possibly reflecting differences in their evolutionary history. Conclusions: The first comparative study of single and binary B-type supergiants has revealed that the main sequence may be significantly wider than previously assumed, extending to Teff = 20 000 K. Some marginal differences in single and binary atmospheric parameters and abundances have been identified, possibly implying non-standard evolution for some of the sample. This sample as a whole has implications for several aspects of our understanding of the evolutionary status of blue supergiants. Tables 1, 4, 7 are available in electronic form at http://www.aanda.org