diff --git a/fsspec/implementations/http.py b/fsspec/implementations/http.py
index ed1794f9b..9e5d20203 100644
--- a/fsspec/implementations/http.py
+++ b/fsspec/implementations/http.py
@@ -696,25 +696,6 @@ async def async_fetch_range(self, start, end):
 
     _fetch_range = sync_wrapper(async_fetch_range)
 
-    def __reduce__(self):
-        return (
-            reopen,
-            (
-                self.fs,
-                self.url,
-                self.mode,
-                self.blocksize,
-                self.cache.name if self.cache else "none",
-                self.size,
-            ),
-        )
-
-
-def reopen(fs, url, mode, blocksize, cache_type, size=None):
-    return fs.open(
-        url, mode=mode, block_size=blocksize, cache_type=cache_type, size=size
-    )
-
 
 magic_check = re.compile("([*[])")
 
@@ -764,9 +745,6 @@ def close(self):
         asyncio.run_coroutine_threadsafe(self._close(), self.loop)
         super().close()
 
-    def __reduce__(self):
-        return reopen, (self.fs, self.url, self.mode, self.blocksize, self.cache.name)
-
 
 class AsyncStreamFile(AbstractAsyncStreamedFile):
     def __init__(
diff --git a/fsspec/spec.py b/fsspec/spec.py
index 6837ab353..4e8d2fdd0 100644
--- a/fsspec/spec.py
+++ b/fsspec/spec.py
@@ -2060,6 +2060,22 @@ def writable(self):
         """Whether opened for writing"""
         return self.mode in {"wb", "ab", "xb"} and not self.closed
 
+    def __reduce__(self):
+        if self.mode != "rb":
+            raise RuntimeError("Pickling a writeable file is not supported")
+
+        return reopen, (
+            self.fs,
+            self.path,
+            self.mode,
+            self.blocksize,
+            self.loc,
+            self.size,
+            self.autocommit,
+            self.cache.name if self.cache else "none",
+            self.kwargs,
+        )
+
     def __del__(self):
         if not self.closed:
             self.close()
@@ -2074,3 +2090,18 @@ def __enter__(self):
 
     def __exit__(self, *args):
         self.close()
+
+
+def reopen(fs, path, mode, blocksize, loc, size, autocommit, cache_type, kwargs):
+    file = fs.open(
+        path,
+        mode=mode,
+        block_size=blocksize,
+        autocommit=autocommit,
+        cache_type=cache_type,
+        size=size,
+        **kwargs,
+    )
+    if loc > 0:
+        file.seek(loc)
+    return file
diff --git a/fsspec/tests/test_spec.py b/fsspec/tests/test_spec.py
index 3927c6550..742f53e06 100644
--- a/fsspec/tests/test_spec.py
+++ b/fsspec/tests/test_spec.py
@@ -15,6 +15,7 @@
 from fsspec.implementations.http import HTTPFileSystem
 from fsspec.implementations.local import LocalFileSystem
 from fsspec.spec import AbstractBufferedFile, AbstractFileSystem
+from fsspec.tests.conftest import data
 
 PATHS_FOR_GLOB_TESTS = (
     {"name": "test0.json", "type": "file", "size": 100},
@@ -744,6 +745,31 @@ def test_cache():
     assert len(DummyTestFS._cache) == 0
 
 
+def test_cache_not_pickled(server):
+    fs = fsspec.filesystem(
+        "http",
+        cache_type="readahead",
+        headers={"give_length": "true", "head_ok": "true"},
+    )
+    filepath = server.realfile
+    length = 3
+    f = fs.open(filepath, mode="rb")
+    assert isinstance(f, AbstractBufferedFile)
+    assert not f.cache.cache  # No cache initially
+    assert f.read(length=length) == data[:length]
+    assert f.cache.cache == data  # Cache is populated
+
+    # Roundtrip through pickle
+    import pickle
+
+    f2 = pickle.loads(pickle.dumps(f))
+    assert not f2.cache.cache  # No cache initially
+    assert (
+        f2.read(length=length) == data[length : 2 * length]
+    )  # Read file from previous seek point
+    assert f2.cache.cache == data[length:]  # Cache is populated
+
+
 def test_current():
     fs = DummyTestFS()
     fs2 = DummyTestFS(arg=1)