Combine multiple partially overlapping rasters into a single raster in R

I have about 1,000 rasters which are around 10km x 10km and partially overlap to cover a whole country.

I would like to convert these into a single national raster, and where raster overlap, add the cell values together.

Currently, I am using ArcGIS's workspace to new raster tool, but I would like to replicate the process in the R language.

I've tried a couple of things but usually end up with only the intersection of the rasters. Many of the solutions on StackExchange advocate cropping to a common area, which is the exact opposite of what I want.

IS there a general solution for aligning two rasters and then making a mosaic which has the combined extent of both rasters?

Can this method be scaled to work for thousands of rasters?

EDIT

> sessionInfo()

R version 3.3.2 (2016-10-31)
Platform: x86_64-w64-mingw32/x64 (64-bit)
Running under: Windows 7 x64 (build 7601) Service Pack 1

locale:
[1] LC_COLLATE=English_United Kingdom.1252  LC_CTYPE=English_United Kingdom.1252    LC_MONETARY=English_United Kingdom.1252
[4] LC_NUMERIC=C                            LC_TIME=English_United Kingdom.1252    

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     


other attached packages:
[1] rgdal_1.2-5  raster_2.5-8 sp_1.2-4    

loaded via a namespace (and not attached):
[1] tools_3.3.2     Rcpp_0.12.9     grid_3.3.2      lattice_0.20-34

> rasterOptions()
format        : raster 
datatype      : FLT8S 

overwrite     : FALSE 
progress      : none 
timer         : FALSE 
chunksize     : 1e+07 
maxmemory     : 1e+08 
tmpdir        : D:/RTemp\RtmpgzISfL/raster/ 
tmptime       : 168 
setfileext    : TRUE 
tolerance     : 0.5 
standardnames : TRUE 

warn depracat.: TRUE 
header        : none

Answer

The best solution to this is making a list of the rasters, then passing this to a function based on the apply family

The following code was pulled from a similar question wrapped into a function and should work for you

mosaicList <- function(rasList){

#Internal function to make a list of raster objects from list of files.
  ListRasters <- function(list_names) {
    raster_list <- list() # initialise the list of rasters

    for (i in 1:(length(list_names))){ 
      grd_name <- list_names[i] # list_names contains all the names of the images in .grd format
      raster_file <- raster::raster(grd_name)
    }
    raster_list <- append(raster_list, raster_file) # update raster_list at each iteration
  }

  #convert every raster path to a raster object and create list of the results
  raster.list <-sapply(rasList, FUN = ListRasters)


  # edit settings of the raster list for use in do.call and mosaic
  names(raster.list) <- NULL
  #####This function deals with overlapping areas
  raster.list$fun <- sum

  #run do call to implement mosaic over the list of raster objects.
  mos <- do.call(raster::mosaic, raster.list)

  #set crs of output
  crs(mos) <- crs(x = raster(rasList[1]))

  return(mos)
}

To use this do something along the lines of:'

raster_files <- list.files(path ="folder_with_files",pattern = ".tif$",full.names = TRUE )

national_layer <- mosaicList(raster_files )