Converting Shapefile coord in projected metres to lat long

Im trying to convert the X Y values (Metres) in a shapefile to degrees but not having much luck. Ive tried trial and error and now really stuck not knowing what I have tried an what not!

Essentially I have the following info from the project file, PROJCS["WGS_1984_World_Mercator",GEOGCS["GCS_WGS_1984",DATUM["D_WGS_1984",SPHEROID["WGS_1984",6378137.0,298.257223563]],PRIMEM["Greenwich",0.0],UNIT["Degree",0.0174532925199433]],PROJECTION["Mercator"],PARAMETER["False_Easting",0.0],PARAMETER["False_Northing",0.0],PARAMETER["Central_Meridian",0.0],PARAMETER["Standard_Parallel_1",0.0],UNIT["Meter",1.0]]

I have tried to use the tool, xyz2ell which is part of the geodetic tool box and have also tried m_xy2ll from another toolbox called m_map. Undoubtedly they work I just dont know the correct config as each gives me incorrect results. If I try use a spherical metres to degrees with the earths circumference I get the correct longitude so I know my actual final reading is correct.

As an example I have the position, -705221.965159964 7422196.68362591 which should be around the west coast of scotland, ~55.47N and -6.36 west.

Would anyone be able to explain how you would perform this operation?

Many thanks Craig.

Answer 1

[KSSV]

Check this file exchange: https://in.mathworks.com/matlabcentral/fileexchange/10914-utm2deg

Answer 2

[Craig]

Thank KSSV but thats for UTM where as my projection is World Mercator. Im pretty sure my problem is how I define the projection when using m_proj or what scale factorto use if trying the simple meractor function, I simply dont understand the variables listed in the proj file and how to use, but reading plenty! Thanks Craig.