Testing consistency between dbamber/UkGeoTool (https://github.com/dbamber/UkGeoTool) and the source by Chris Veness (http://www.movable-type.co.uk/scripts/latlong-gridref.html). With easting 510350 / northing 179950 as an input, the first function outputs { latitude: 51.50721000898611, longitude: -0.40978487356944765 } , while the second { lat: …

The original function by Chris Veness, made into a standalone script for testing

// Source http://www.movable-type.co.uk/scripts/latlong-gridref.html 

Number.prototype.toDeg = function() {  // convert radians to degrees (signed)
  return this * 180 / Math.PI;
}

osGridToLatLong = function(gridref) {
  var E = gridref.easting;
  var N = gridref.northing;

  var a = 6377563.396, b = 6356256.910;              // Airy 1830 major & minor semi-axes
  var F0 = 0.9996012717;                             // NatGrid scale factor on central meridian
  var lat0 = 49*Math.PI/180, lon0 = -2*Math.PI/180;  // NatGrid true origin
  var N0 = -100000, E0 = 400000;                     // northing & easting of true origin, metres
  var e2 = 1 - (b*b)/(a*a);                          // eccentricity squared
  var n = (a-b)/(a+b), n2 = n*n, n3 = n*n*n;

  var lat=lat0, M=0;
  do {
    lat = (N-N0-M)/(a*F0) + lat;

    var Ma = (1 + n + (5/4)*n2 + (5/4)*n3) * (lat-lat0);
    var Mb = (3*n + 3*n*n + (21/8)*n3) * Math.sin(lat-lat0) * Math.cos(lat+lat0);
    var Mc = ((15/8)*n2 + (15/8)*n3) * Math.sin(2*(lat-lat0)) * Math.cos(2*(lat+lat0));
    var Md = (35/24)*n3 * Math.sin(3*(lat-lat0)) * Math.cos(3*(lat+lat0));
    M = b * F0 * (Ma - Mb + Mc - Md);                // meridional arc

  } while (N-N0-M >= 0.00001);  // ie until < 0.01mm

  var cosLat = Math.cos(lat), sinLat = Math.sin(lat);
  var nu = a*F0/Math.sqrt(1-e2*sinLat*sinLat);              // transverse radius of curvature
  var rho = a*F0*(1-e2)/Math.pow(1-e2*sinLat*sinLat, 1.5);  // meridional radius of curvature
  var eta2 = nu/rho-1;

  var tanLat = Math.tan(lat);
  var tan2lat = tanLat*tanLat, tan4lat = tan2lat*tan2lat, tan6lat = tan4lat*tan2lat;
  var secLat = 1/cosLat;
  var nu3 = nu*nu*nu, nu5 = nu3*nu*nu, nu7 = nu5*nu*nu;
  var VII = tanLat/(2*rho*nu);
  var VIII = tanLat/(24*rho*nu3)*(5+3*tan2lat+eta2-9*tan2lat*eta2);
  var IX = tanLat/(720*rho*nu5)*(61+90*tan2lat+45*tan4lat);
  var X = secLat/nu;
  var XI = secLat/(6*nu3)*(nu/rho+2*tan2lat);
  var XII = secLat/(120*nu5)*(5+28*tan2lat+24*tan4lat);
  var XIIA = secLat/(5040*nu7)*(61+662*tan2lat+1320*tan4lat+720*tan6lat);

  var dE = (E-E0), dE2 = dE*dE, dE3 = dE2*dE, dE4 = dE2*dE2, dE5 = dE3*dE2, dE6 = dE4*dE2, dE7 = dE5*dE2;
  lat = lat - VII*dE2 + VIII*dE4 - IX*dE6;
  var lon = lon0 + X*dE - XI*dE3 + XII*dE5 - XIIA*dE7;
  
  return { latitude: lat.toDeg(), longitude: lon.toDeg() };
}


console.log(osGridToLatLong({ easting: 510350., northing: 179950. }));

The same, using UKGeoTool

var geo = require('UkGeoTool'); // https://github.com/dbamber/UkGeoTool
var point = { easting: 510350., northing: 179950. };
console.log(geo.eastNorthToLatLong(point.northing, point.easting));