Edit - Update with OSGB36 specific information.
Well, the good news is that the target projection is OSGB36, which is a well known and standardized projection. The bad news is that GIS programming is still really difficult :)
There are a set of parameters that need to be defined, and mathematical operations applied to those parameters, to succesfully project lat/long to grids. Fortunately, there are databases of parameters for the former, and libraries for the latter.
proj.4, which I mentioned earlier, is one of the standard libraries. There are also ports of
The other thing you need to know is the
EPSG number for your coordinate systems. OSGB36 is EPSG:6277. The EPSG is an oil-industry (I think) created body that collected lots of locally defined projections and documented them. The database is now openly maintained, and GIS libraries can use their definitions.
Your easting/northing numbers may be in the British national grid system.
I gave an answer to another GIS related question that includes links to
proj.4, which is one of the standard libraries for converting between lat/long and easting/northing (the forward calculation is called
projection in the GIS world). I've never used it for the conversion you're looking for, but the software is well-documented and comes with conversion definitions for lots of projections.