Converting raster stack extent from meters to lat/lon coordinates

I have a raster stack in the following format which I converted to NetCDF using this method. This works but the latitude and longitude variables are in 'meters' which is the extent of the raster file, and I need them to be in decimal degrees. The R Grid file is here and the format is as follows:

class       : RasterBrick 
dimensions  : 205, 170, 34850, 12  (nrow, ncol, ncell, nlayers)
resolution  : 1, 1  (x, y)
extent      : 160.5, 330.5, 145.5, 350.5  (xmin, xmax, ymin, ymax)
coord. ref. : NA 
data source : \TavgM_1981.grd 
names       :   Jan.1981,   Feb.1981,   Mar.1981,   Apr.1981,   May.1981,   Jun.1981,   Jul.1981,   Aug.1981,   Sep.1981,   Oct.1981,   Nov.1981,   Dec.1981 
min values  :  1.9912137,  0.8120775,  4.0446638,  4.4135274,  6.5349769,  8.6149150,  9.9991916, 11.8400562,  9.6407796,  3.5005649,  4.1205872, -0.6106244 
max values  :   9.850221,   9.121176,  10.238524,   9.858942,  11.669445,  14.260988,  15.722292,  17.235090,  15.708690,  11.598482,  11.552235,   8.981533 
time        : Jan 1981, Feb 1981, Mar 1981, Apr 1981, May 1981, Jun 1981, Jul 1981, Aug 1981, Sep 1981, Oct 1981, Nov 1981, Dec 1981 

Ideally I would like to convert this to a NetCDF file which has the following format to be read by a model:

Dimensions:    (lat: 408, lon: 881, nb2: 2, time: 660)
Coordinates:
  * lon        (lon) float64 -44.81 -44.69 -44.56 -44.44 -44.31 -44.19 ...
  * lat        (lat) float64 21.81 21.94 22.06 22.19 22.31 22.44 22.56 22.69 ...
  * time       (time) datetime64[ns] 1951-01-16T12:00:00 1951-02-16T12:00:00 ...
Dimensions without coordinates: nb2
Data variables:
    time_bnds  (time, nb2) datetime64[ns] 1951-01-16T12:00:00 ...
    tas        (time, lat, lon) float64 nan nan nan nan nan nan nan nan nan ...

I tried to convert the Raster Brick extent to lat/lon using this method:

sputm <- SpatialPoints(test@extent@xmin, proj4string=CRS("+proj=utm +zone=29N +datum=WGS84"))

But this gives this error:

Error in (function (classes, fdef, mtable)  : unable to find an inherited method for function ‘coordinates’ for signature ‘"numeric"’

EDIT: Also tried

crs(test) <- '+proj=merc +datum=WGS84'
x <- projectRaster(test, crs='+proj=longlat +datum=WGS84') 

writeRaster(x, "rstack2.nc", overwrite=TRUE, format="CDF",     varname="Temperature", varunit="degC", 
        longname="Temperature -- raster stack to netCDF", xname="Longitude",   yname="Latitude", zname="Time (Month)")

But when I examine this in panoply the lat and lon coordinates are all 0.0.

I'm not sure where to go from here.

As fas as I recognized Ireland, I looked at Ireland projections. I think this is the TM75 / Irish Grid. I modified the resolution of your raster so that it is 2500m.

library(raster)

r <- stack("~/Bureau/TavgM_1981")
xmax(r) <- xmin(r) + 2500 * ncol(r)
ymax(r) <- ymin(r) + 2500 * nrow(r)

crs(r) <- "+proj=tmerc +lat_0=53.5 +lon_0=-8 +k=1.000035 +x_0=200000 +y_0=250000 +ellps=mod_airy +towgs84=482.5,-130.6,564.6,-1.042,-0.214,-0.631,8.15 +units=m +no_defs"

# Convert to degrees
x_wgs84 <- projectRaster(r, crs='+proj=longlat +datum=WGS84') 

writeRaster(x, "~/Bureau/TavgM_wgs84.tif", overwrite = TRUE)

You will see below the result of this resolution + projection modification compared to the target.
We are not so far from reality but there is something bad in your original raster. If this is (unfortunately) usual not to have the crs when somebody gives you a layer, this is not usual to miss the correct resolution.
As the raster you provide is saved as ".gri/.grd" file, this means that it has been produced with R. You should try to get the original R code that produced the file, instead of the final modified layer.