There are many predefined transformations available in ArcGIS  to transform between OSGB36 and WGS84. These range from very accurate (+/- 2m) to relatively inaccurate (+/- 35m), depending on where you are.
NOTE: If you do not select a transformation, ArcGIS will still transform the data but not do a datum shift with a resulting accuracy of over 100m .
Figure 4: ArcGIS Transformations
A complete list of transformations available in ArcGIS and their accuracies is available on the Esri Resource Centre.
Usually the recommended transformation to use that is built into ArcGIS is the OSGB_1936_To_WGS_1984_Petroleum one (this uses the same parameters as the 7 parameter shift recommended by Ordnance Survey). This has an accuracy of +/- 5m.
However, if a more accurate transformation is required, the Ordnance Survey OSTN02 transformation should be used.
By default ArcGIS does not contain the OSTN02 transformation from Ordnance Survey that should be used to convert data from OSGB36 to WGS84 for the highest accuracy; however in ArcGIS 10.x it is simple to implement (note you only need to do this once):
a) Download the grid shift file from Ordnance Survey
OSTN02 data file
b) Extract and copy the file OSTN02_NTv2.gsb to the folder:
"C:\Program Files (x86)\ArcGIS\Desktop10.2\pedata\ntv2\uk" (or equivalent installation folder, e.g. replace 10.3 for 10.2 if you are running 10.3)
c) Note you will need to create the ’uk’ (lowercase) folder as a subfolder of ntv2.
d) On reloading ArcGIS (or just reopening the Trransformations dialog) you will notice a transformation available if you choose OSGB36 to WGS84 called OSGB_1936_To_WGS_1984_7 that is using the OSTN_02 method.
Figure 5: ArcGIS using OSTN02
If you don’t use the OSTN02 method you should use the OSGB_1936_To_WGS_1984_Petroleum transformation. You should always explicitly choose a transformation and never accept the default!
 eLearning module on Coordinate systems and projections: http://digimap.edina.ac.uk/webhelp/training/training.htm#elearning/eLearning.htm
 Ordnance Survey – A Guide to coordinate systems in Great Britain
 Seazone: Introduction to Coordinate Reference Systems
 Coordinate Systems in FME: https://knowledge.safe.com/articles/585/using-coordinate-systems-within-fme.html
Geotrans Geographic Translator
Defining Coordinate Systems in FME: http://docs.safe.com/fme/html/FME_Desktop_Documentation/FME_Coordinate_Systems/Home_cs.htm
Esri UK – Understanding which Transformation to Choose in ArcGIS: http://communityhub.esriuk.com/journal/2012/3/26/coordinate-systems-and-projections-for-beginners.html
 Esri UK – What are my OGC web services displaced by about 120m?: http://communityhub.esriuk.com/journal/2012/10/12/why-are-my-ogc-web-services-displaced-by-about-120-metres.html
 Other information about implementing OSTN02 in PostGIS directly is available here:
 Information about transformations in QGIS
 Blog from Frank Warmerdam indicating how transformations are chosen in proj.4
 PROJ.4 General Parameters