In base R we can do :
df[] <- lapply(df, as.numeric)
or
df[cols_to_convert]  <- lapply(df[cols_to_convert], as.numeric)
Here's a benchmark of the solutions (ignoring the considerations about factors) :
DF <- data.frame(a = 1:10000, b = letters[1:10000],
                 c = seq(as.Date("2004-01-01"), by = "week", len = 10000),
                 stringsAsFactors = TRUE)
DF <- setNames(do.call(cbind,replicate(50,DF,simplify = F)),paste0("V",1:150))
dim(DF)
# [1] 10000   150
library(dplyr)
n1tk  <- function(x) data.frame(data.matrix(x))
mm    <- function(x) {x[] <- lapply(x,as.numeric); x}
akrun <- function(x) mutate_all(x, as.numeric)
mo    <- function(x)  {for(i in 1:150){ x[, i] <- as.numeric(x[, i])}}
microbenchmark::microbenchmark(
  akrun = akrun(DF),
  n1tk  = n1tk(DF),
  mo    = mo(DF),
  mm    = mm(DF)
)
# Unit: milliseconds
#   expr      min        lq       mean    median        uq      max neval
#  akrun 152.9837 177.48150 198.292412 190.38610 206.56800 432.2679   100
#   n1tk  10.8700  14.48015  22.632782  17.43660  21.68520  89.4694   100
#     mo   9.3512  11.41880  15.313889  14.71970  17.66530  37.6390   100
#     mm   4.8294   5.91975   8.906348   7.80095  10.11335  71.2647   100