diff --git a/fstest/mockobject/mockobject.go b/fstest/mockobject/mockobject.go
index 084536b85..dad56a634 100644
--- a/fstest/mockobject/mockobject.go
+++ b/fstest/mockobject/mockobject.go
@@ -93,13 +93,14 @@ const (
 // SeekModes contains all valid SeekMode's
 var SeekModes = []SeekMode{SeekModeNone, SeekModeRegular, SeekModeRange}
 
-// ContentMockObject mocks an fs.Object and has content
+// ContentMockObject mocks an fs.Object and has content, mod time
 type ContentMockObject struct {
 	Object
 	content     []byte
 	seekMode    SeekMode
 	f           fs.Fs
 	unknownSize bool
+	modTime     time.Time
 }
 
 // WithContent returns an fs.Object with the given content.
@@ -192,6 +193,18 @@ func (o *ContentMockObject) Hash(ctx context.Context, t hash.Type) (string, erro
 	return hasher.Sums()[t], nil
 }
 
+// ModTime returns the modification date of the file
+// It should return a best guess if one isn't available
+func (o *ContentMockObject) ModTime(ctx context.Context) time.Time {
+	return o.modTime
+}
+
+// SetModTime sets the metadata on the object to set the modification date
+func (o *ContentMockObject) SetModTime(ctx context.Context, t time.Time) error {
+	o.modTime = t
+	return nil
+}
+
 type readCloser struct{ io.Reader }
 
 func (r *readCloser) Close() error { return nil }
diff --git a/lib/http/serve/serve.go b/lib/http/serve/serve.go
index c4b70f1fd..6f97d0d8a 100644
--- a/lib/http/serve/serve.go
+++ b/lib/http/serve/serve.go
@@ -35,6 +35,10 @@ func Object(w http.ResponseWriter, r *http.Request, o fs.Object) {
 		w.Header().Set("Content-Type", mimeType)
 	}
 
+	// Set last modified
+	modTime := o.ModTime(r.Context())
+	w.Header().Set("Last-Modified", modTime.UTC().Format(http.TimeFormat))
+
 	if r.Method == "HEAD" {
 		return
 	}
diff --git a/lib/http/serve/serve_test.go b/lib/http/serve/serve_test.go
index b6cc70976..dc9098428 100644
--- a/lib/http/serve/serve_test.go
+++ b/lib/http/serve/serve_test.go
@@ -1,10 +1,12 @@
 package serve
 
 import (
+	"context"
 	"io"
 	"net/http"
 	"net/http/httptest"
 	"testing"
+	"time"
 
 	"github.com/rclone/rclone/fstest/mockobject"
 	"github.com/stretchr/testify/assert"
@@ -25,11 +27,13 @@ func TestObjectHEAD(t *testing.T) {
 	w := httptest.NewRecorder()
 	r := httptest.NewRequest("HEAD", "http://example.com/aFile", nil)
 	o := mockobject.New("aFile").WithContent([]byte("hello"), mockobject.SeekModeNone)
+	_ = o.SetModTime(context.Background(), time.Date(2023, 9, 20, 12, 11, 15, 0, time.FixedZone("", 4*60*60))) // UTC+4
 	Object(w, r, o)
 	resp := w.Result()
 	assert.Equal(t, http.StatusOK, resp.StatusCode)
 	assert.Equal(t, "5", resp.Header.Get("Content-Length"))
 	assert.Equal(t, "bytes", resp.Header.Get("Accept-Ranges"))
+	assert.Equal(t, "Wed, 20 Sep 2023 08:11:15 GMT", resp.Header.Get("Last-Modified"))
 	body, _ := io.ReadAll(resp.Body)
 	assert.Equal(t, "", string(body))
 }
@@ -38,11 +42,13 @@ func TestObjectGET(t *testing.T) {
 	w := httptest.NewRecorder()
 	r := httptest.NewRequest("GET", "http://example.com/aFile", nil)
 	o := mockobject.New("aFile").WithContent([]byte("hello"), mockobject.SeekModeNone)
+	_ = o.SetModTime(context.Background(), time.Date(2023, 9, 20, 12, 11, 15, 0, time.FixedZone("", 2*60*60))) // UTC+2
 	Object(w, r, o)
 	resp := w.Result()
 	assert.Equal(t, http.StatusOK, resp.StatusCode)
 	assert.Equal(t, "5", resp.Header.Get("Content-Length"))
 	assert.Equal(t, "bytes", resp.Header.Get("Accept-Ranges"))
+	assert.Equal(t, "Wed, 20 Sep 2023 10:11:15 GMT", resp.Header.Get("Last-Modified"))
 	body, _ := io.ReadAll(resp.Body)
 	assert.Equal(t, "hello", string(body))
 }