how to make a data frame into a simple features data frame?

Your attempt and the accepted answers are unnecessarily complicated and terribly confusing. Just go with st_as_sf (which by the way also easily migrates all objects from the outdated sp class (SpatialPolygonsDataFrames and the like)):

df <- data.frame(place = "London", 
       lat = 51.5074, lon = 0.1278,
       population = 8500000) # just to add some value that is plotable
projcrs <- "+proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0"
df <- st_as_sf(x = df,                         
           coords = c("lon", "lat"),
           crs = projcrs)

And we are done, as easy as that.

Just to visualise it:

library(tmap)
data("World")    
tm_shape(World[World$iso_a3 == "GBR", ]) + tm_polygons("pop_est") + 
    tm_shape(df) + tm_bubbles("population")

Or with the new amazing geom_sf from ggplot2:

library(ggplot2)
ggplot(World) + geom_sf() + geom_sf(data = df, shape = 4, col = "red", size = 5)

UPDATE The answer from @Franz Plumpton is the correct correct solution with a single epsg. My answer below is only necessary when each row of a data.frame has a different epsg. Otherwise, this would be a duplicate (as pointed out by @Henrik above).

library(sf)
library(tibble)

df <- data_frame(place = c("London", "Kalamazoo"), 
           lat = c(51.5074, 396088), lon = c(0.1278, 5452158),
           epsg = c(4326, 32610))

l <- lapply(unique(df$place), function(x){
  df <- df[df$place == x,]
  epsg <- df$epsg[1]
  df  <-  st_as_sf(df, coords = c('lon', 'lat'), crs = epsg)
}) 

you could then transform all to the same epsg and combine into a single data.frame:

do.call(rbind, lapply(l, function(x) x <- st_transform(x, 4326)))