I have a point dataset expressed in British National Grid (about 10,000 points distributed all over the UK). I want to do some cluster analysis and I am aware that distance distortion might have an effect on the results. The precision I need is quite coarse (about 200m-500m). Do I need to take steps in the analysis or can I just calculate Euclidean distances?
Using NUTS-3 centroids with the Near (Analysis) tool, the geodetic distance between the Shetland Islands and Jersey was calculated to be 1191878.03 meters. Using a Euclidean distance after projecting to British National Grid (with the default datum transformation), those two points are 1191362.07 meters apart (a delta of 515.96 meters, or 0.043 percent).
The distance between the centroids of Westminster and Edinburgh is 532,119.78 (geodetic) and 531,949.88 (Euclidean) with a difference of 169.90m (0.032%), and between Westminster and Belfast is 519,194.12 (geodetic) and 519,162.44 (Euclidean), with a difference of 31.69 meters (0.006%). Using closer points, Sheffield and Westminster are 229,965.15m (geodetic) and 229,897.19m (Euclidean) apart, with a difference of 67.96m (0.030%)
So, with just four samples, it seems the intrinsic error over the British National Grid is not more than 0.05%, which hovers close to your desired precision. You'll probably want to run the numbers both ways in your analysis, then make your choice from there.