Previous analyses of the spectra of OB-type stars in the Magellanic Clouds have identified targets with low projected rotational velocities and relatively high nitrogen abundances; the evolutionary status of these objects remains unclear. The VLT-FLAMES Tarantula Survey obtained spectroscopy for over 800 early-type stars in 30 Doradus of which 434 stars were classified as B-type. We have estimated atmospheric parameters and nitrogen abundances using TLUSTY model atmospheres for 54 B-type targets that appear to be single, have projected rotational velocities, ve sin i ≤ 80 km s-1 and were not classified as supergiants. In addition, nitrogen abundances for 34 similar stars observed in a previous FLAMES survey of the Large Magellanic Cloud have been re-evaluated. For both samples, approximately 75-80% of the targets have nitrogen enhancements of less than 0.3 dex, consistent with them having experienced only small amounts of mixing. However, stars with low projected rotational velocities, ve sini ≤ 40 km s-1 and significant nitrogen enrichments are found in both our samples and simulations imply that these cannot all be rapidly rotating objects observed near pole-on. For example, adopting an enhancement threshold of 0.6 dex, we observed five and four stars in our VFTS and previous FLAMES survey samples, yet stellar evolution models with rotation predict only 1.25 ± 1.11 and 0.26 ± 0.51 based on our sample sizes and random stellar viewing inclinations. The excess of such objects is estimated to be 20-30% of all stars with current rotational velocities of less than 40 km s-1. This would correspond to 2-4% of the total non-supergiant single B-type sample. Given the relatively large nitrogen enhancement adopted, these estimates constitute lower limits for stars that appear inconsistent with current grids of stellar evolutionary models. Including targets with smaller nitrogen enhancements of greater than 0.2 dex implies larger percentages of targets that are inconsistent with current evolutionary models, viz. 70% of the stars with rotational velocities less than 40 km s-1 and 6-8% of the total single stellar population. We consider possible explanations of which the most promising would appear to be breaking due to magnetic fields or stellar mergers with subsequent magnetic braking. Based on observations at the European Southern Observatory in programmes 171.D0237, 073.D0234 and 182.D-0222.