diff --git a/NEWS.md b/NEWS.md
index 5d9e163ad..87bd4790f 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -52,6 +52,8 @@
 
 10. `fread()` no longer misreads dates with negative years, [#7704](https://github.com/Rdatatable/data.table/issues/7704). Thanks to @kevinushey for the report and @aitap for the fix.
 
+11. `fread()` would not give a warning when every second line of input was empty, [#3339](https://github.com/Rdatatable/data.table/issues/3339). Now, a warning message 'The rows in this file appear to be separated by blank lines.' is given and suggests to set `blank.lines.skip` to `TRUE`. Thanks to @Henrik-P for the report and @Asa-Henry for the fix.
+
 ### Notes
 
 1. {data.table} now depends on R 3.5.0 (2018).
diff --git a/inst/tests/tests.Rraw b/inst/tests/tests.Rraw
index 1b5ea162a..3d11b77b8 100644
--- a/inst/tests/tests.Rraw
+++ b/inst/tests/tests.Rraw
@@ -8059,20 +8059,22 @@ test(1577.3, levels(X$b), character(0))
 
 # FR #530, skip blank lines
 input = "Header not 2 columns\n\n1,3\n2,4"
-test(1578.1, fread(input), data.table(V1=1:2, V2=3:4))
+test(1578.01, fread(input), data.table(V1=1:2, V2=3:4))
 input = "a,b\n\n1,3\n2,4"
-test(1578.2, fread(input), data.table(V1=1:2, V2=3:4))  # the block of 2x2 dominates the one line with sep in auto-removed header section
-test(1578.3, fread(input, blank.lines.skip=TRUE), data.table( a=1:2,  b=3:4))
+test(1578.02, fread(input), data.table(V1=1:2, V2=3:4))  # the block of 2x2 dominates the one line with sep in auto-removed header section
+test(1578.03, fread(input, blank.lines.skip=TRUE), data.table( a=1:2,  b=3:4))
 input = "a,b\n\n\n1,3\n2,4"
-test(1578.4, fread(input, blank.lines.skip=TRUE), data.table( a=1:2,  b=3:4))
+test(1578.04, fread(input, blank.lines.skip=TRUE), data.table( a=1:2,  b=3:4))
 input = "a,b\n\n\n1,3\n\n2,4\n\n"
-test(1578.5, fread(input, blank.lines.skip=TRUE), data.table( a=1:2,  b=3:4))
+test(1578.05, fread(input, blank.lines.skip=TRUE), data.table( a=1:2,  b=3:4))
 
 f = testDir("530_fread.txt")
-test(1578.6, fread(f, skip=47L, verbose=TRUE), data.table(V1=1:2, V2=3:4), output="Positioned on line 48 starting: <<a,b>>")
-test(1578.7, fread(f, skip=49L), data.table(V1=1:2, V2=3:4))
-test(1578.8, fread(f, skip=47L, blank.lines.skip=TRUE), data.table(a=1:2, b=3:4))
-test(1578.9, fread(f, skip=48L), data.table(V1=1:2, V2=3:4))  # start on blank line 49 and skip="auto" to first data row on line 50
+test(1578.06, fread(f, skip=47L, verbose=TRUE), data.table(V1=1:2, V2=3:4), output="Positioned on line 48 starting: <<a,b>>")
+test(1578.07, fread(f, skip=49L), data.table(V1=1:2, V2=3:4))
+test(1578.08, fread(f, skip=47L, blank.lines.skip=TRUE), data.table(a=1:2, b=3:4))
+test(1578.09, fread(f, skip=48L), data.table(V1=1:2, V2=3:4))  # start on blank line 49 and skip="auto" to first data row on line 50
+input = "x y\n\n1 a\n\n2 b\n\n3 c"
+test(1578.10, fread(input), data.table(V1=3L, V2="c"), warning="The rows in this file appear to be separated by blank lines. This resulted in most rows being skipped. If this was not the intended outcome, please consider setting 'blank.lines.skip' to TRUE.")
 
 # test 1579 moved to optimize.Rraw
 
diff --git a/src/fread.c b/src/fread.c
index 70125ec32..a017c18f3 100644
--- a/src/fread.c
+++ b/src/fread.c
@@ -1847,6 +1847,7 @@ int freadMain(freadMainArgs _args)
       int topNumFields = 1;               // how many fields that was, to resolve ties
       enum quote_rule_t topQuoteRule = -1;   // which quote rule that was
       int topSkip = 0;                    // how many rows to auto-skip
+      // #7707 'topSkip' accumulates as blank lines are encountered; can be used to differentiate between a file where the header and data are separated by a blank line and a file where block(s) of lines or each line is separated by a blank line
       const char *topStart = NULL;
     
       for (quoteRule = quote ? QUOTE_RULE_EMBEDDED_QUOTES_DOUBLED : QUOTE_RULE_IGNORE_QUOTES; quoteRule < QUOTE_RULE_COUNT; quoteRule++) { // #loop_counter_not_local_scope_ok
@@ -1950,6 +1951,10 @@ int freadMain(freadMainArgs _args)
           }
         }
       }
+      if (!prevStart && topSkip > 1 && !skipEmptyLines)
+      {
+        DTWARN(_("The rows in this file appear to be separated by blank lines. This resulted in most rows being skipped. If this was not the intended outcome, please consider setting 'blank.lines.skip' to TRUE.\n"));
+      }
       if (!firstJumpEnd) {
         if (verbose) DTPRINT(_("  No sep and quote rule found a block of 2x2 or greater. Single column input.\n"));
         topNumFields = 1;