diff --git a/src/poetry/installation/chooser.py b/src/poetry/installation/chooser.py
index b484504ed9a..4601189d16d 100644
--- a/src/poetry/installation/chooser.py
+++ b/src/poetry/installation/chooser.py
@@ -8,6 +8,7 @@
 
 from poetry.config.config import Config
 from poetry.config.config import PackageFilterPolicy
+from poetry.repositories.http_repository import HTTPRepository
 from poetry.utils.wheel import Wheel
 
 
@@ -103,6 +104,12 @@ def _get_links(self, package: Package) -> list[Link]:
 
             assert link.hash_name is not None
             h = link.hash_name + ":" + link.hash
+            if (
+                h not in hashes
+                and link.hash_name not in ("sha256", "sha384", "sha512")
+                and isinstance(repository, HTTPRepository)
+            ):
+                h = repository.calculate_sha256(link) or h
             if h not in hashes:
                 logger.debug(
                     "Skipping %s as %s checksum does not match expected value",
diff --git a/src/poetry/repositories/http_repository.py b/src/poetry/repositories/http_repository.py
index 9427d72bfe7..ebf8b1a4d77 100644
--- a/src/poetry/repositories/http_repository.py
+++ b/src/poetry/repositories/http_repository.py
@@ -226,24 +226,7 @@ def _links_to_data(self, links: list[Link], data: PackageInfo) -> dict[str, Any]
                 and link.hash_name not in ("sha256", "sha384", "sha512")
                 and hasattr(hashlib, link.hash_name)
             ):
-                with self._cached_or_downloaded_file(link) as filepath:
-                    known_hash = (
-                        getattr(hashlib, link.hash_name)() if link.hash_name else None
-                    )
-                    required_hash = hashlib.sha256()
-
-                    chunksize = 4096
-                    with filepath.open("rb") as f:
-                        while True:
-                            chunk = f.read(chunksize)
-                            if not chunk:
-                                break
-                            if known_hash:
-                                known_hash.update(chunk)
-                            required_hash.update(chunk)
-
-                    if not known_hash or known_hash.hexdigest() == link.hash:
-                        file_hash = f"{required_hash.name}:{required_hash.hexdigest()}"
+                file_hash = self.calculate_sha256(link) or file_hash
 
             files.append({"file": link.filename, "hash": file_hash})
 
@@ -257,6 +240,25 @@ def _links_to_data(self, links: list[Link], data: PackageInfo) -> dict[str, Any]
 
         return data.asdict()
 
+    def calculate_sha256(self, link: Link) -> str | None:
+        with self._cached_or_downloaded_file(link) as filepath:
+            known_hash = getattr(hashlib, link.hash_name)() if link.hash_name else None
+            required_hash = hashlib.sha256()
+
+            chunksize = 4096
+            with filepath.open("rb") as f:
+                while True:
+                    chunk = f.read(chunksize)
+                    if not chunk:
+                        break
+                    if known_hash:
+                        known_hash.update(chunk)
+                    required_hash.update(chunk)
+
+            if not known_hash or known_hash.hexdigest() == link.hash:
+                return f"{required_hash.name}:{required_hash.hexdigest()}"
+        return None
+
     def _get_response(self, endpoint: str) -> requests.Response | None:
         url = self._url + endpoint
         try:
diff --git a/tests/helpers.py b/tests/helpers.py
index eefe9c74c1a..3dd5b1d8915 100644
--- a/tests/helpers.py
+++ b/tests/helpers.py
@@ -36,6 +36,7 @@
 
     from poetry.installation.operations.operation import Operation
     from poetry.poetry import Poetry
+    from poetry.utils.authenticator import Authenticator
 
 FIXTURE_PATH = Path(__file__).parent / "fixtures"
 
@@ -120,7 +121,7 @@ def mock_clone(
     return MockDulwichRepo(dest)
 
 
-def mock_download(url: str, dest: Path) -> None:
+def mock_download(url: str, dest: Path, session: Authenticator | None = None) -> None:
     parts = urllib.parse.urlparse(url)
 
     fixture = FIXTURE_PATH / parts.path.lstrip("/")
diff --git a/tests/installation/test_chooser.py b/tests/installation/test_chooser.py
index fbd3861ad05..6c9930f899a 100644
--- a/tests/installation/test_chooser.py
+++ b/tests/installation/test_chooser.py
@@ -405,3 +405,25 @@ def test_chooser_throws_an_error_if_package_hashes_do_not_match(
     with pytest.raises(RuntimeError) as e:
         chooser.choose_for(package)
     assert files[0]["hash"] in str(e)
+
+
+@pytest.mark.usefixtures("mock_legacy")
+def test_chooser_md5_remote_fallback_to_sha256_inline_calculation(
+    env: MockEnv, pool: RepositoryPool
+) -> None:
+    chooser = Chooser(pool, env)
+    package = Package(
+        "demo",
+        "0.1.0",
+        source_type="legacy",
+        source_reference="foo",
+        source_url="https://foo.bar/simple/",
+    )
+    package.files = [
+        {
+            "hash": "sha256:9fa123ad707a5c6c944743bf3e11a0e80d86cb518d3cf25320866ca3ef43e2ad",  # noqa: E501
+            "filename": "demo-0.1.0.tar.gz",
+        }
+    ]
+    res = chooser.choose_for(package)
+    assert res.filename == "demo-0.1.0.tar.gz"
diff --git a/tests/repositories/fixtures/legacy/demo.html b/tests/repositories/fixtures/legacy/demo.html
new file mode 100644
index 00000000000..ae9506cd5a1
--- /dev/null
+++ b/tests/repositories/fixtures/legacy/demo.html
@@ -0,0 +1,6 @@
+<html>
+<head><title>Simple Index</title><meta name="api-version" value="2" /></head>
+<body>
+<a href="https://files.pythonhosted.org/distributions/demo-0.1.0.tar.gz#md5=d1912c917363a64e127318655f7d1fe7" rel="internal">demo-0.1.0.tar.gz</a><br/>
+</body>
+</html>