update easting and northing using distance and bearing

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Unfortunately I'm not familiar with OSGB70, as I normally deal with OSGB70 & WGS84. However:

OSGB70 & ODGB36 share the same ellipsoid:
OSGB70: http://www.eye4software.com/products/coordinatecalculator/datum/175/
OSGB36: http://www.eye4software.com/products/coordinatecalculator/datum/12/

This page gives you some idea of how to do the transformation:
http://www.linz.govt.nz/geodetic/conversion-coordinates/geodetic-datum-conversion/datum-transformation-equations/index.aspx

The nice thing is that as the transformation and rotation parameters are all zero (for WGS84 & OSGB70), you only have to convert your coordinates in OSGB70 to Cartesian (using the Airy ellipsoid), and then straight back to WGS84 coordinates (using the WGS84 ellipsoid).
Actually, I'm guessing that your data is already cartesian coordinates as you mentioned Eastings & Northings, so you should only have to use the ToWGS84 method.

Then operating on the WGS84 using the equations in the 1st set of links I posted.

private static void FromOSGB70(double lat, double lon, double h,
  out double x, out double y, out double z) {
  // WGS coordinates in radians
  double phi = lat * Math.PI / 180;
  double lambda = lon * Math.PI / 180;
 
  // Airy 1830 ellipsoid parameters
  // http://www.eye4software.com/products/coordinatecalculator/datum/175/
  // Semi-major axis
  double a = 6377563.396;
  // Flattening
  double f = 1 / 299.3249646;
  // Eccentricity squared
  double e2 = (2 * f) - (f * f);
 
  double nu = a / Math.Sqrt(1 - e2 * Math.Pow(Math.Sin(phi), 2));
 
  x = (nu + h) * Math.Cos(phi) * Math.Cos(lambda);
  y = (nu + h) * Math.Cos(phi) * Math.Sin(lambda);
  z = ((nu * (1 - e2)) + h) * Math.Sin(phi);
}
 
private static void ToWGS84(double x, double y, double z,
  out double lat, out double lon, out double h) {
  // WGS84 ellipsoid parameters
  // http://www.eye4software.com/products/coordinatecalculator/datum/7/
  // Semi-major axis
  double a = 6378137;
  // Flattening
  double f = 1 / 298.257223563;
  // Eccentricity squared
  double e2 = (2 * f) - (f * f);
   
  double p = Math.Sqrt((x * x) + (y * y));
  double r = Math.Sqrt((p * p) + (z * z));
  double mu = Math.Atan2(
    z * ((1 - f) + (e2 * a / r)),
    p
    );
 
  double lambda= Math.Atan2(y, x);
  double phi = Math.Atan2(
    (z * (1 - f)) + (e2 * a * Math.Pow(Math.Sin(mu), 3)),
    (1 - f) * (p - (e2 * a * Math.Pow(Math.Cos(mu), 3)))
    );
  h = (p * Math.Cos(phi)) + (z * Math.Sin(phi)) -
    (a * Math.Sqrt(1 - (e2 * Math.Pow(Math.Sin(phi), 2))));
 
  lat = phi * 180 / Math.PI;
  lon = lambda * 180 / Math.PI;
}

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update easting and northing using distance and bearing

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