GetResponseAsync does not accept cancellationToken

Something like this should work (untested):

public static class Extensions
{
    public static async Task<HttpWebResponse> GetResponseAsync(this HttpWebRequest request, CancellationToken ct)
    {
        using (ct.Register(() => request.Abort(), useSynchronizationContext: false))
        {
            var response = await request.GetResponseAsync();
            ct.ThrowIfCancellationRequested();
            return (HttpWebResponse)response;
        }
    }
}

In theory, if cancellation is requested on ct and request.Abort is invoked, await request.GetResponseAsync() should throw a WebException. IMO though, it’s always a good idea to check for cancellation explicitly when consuming the result, to mitigate race conditions, so I call ct.ThrowIfCancellationRequested().

Also, I assume that request.Abort is thread-safe (can be called from any thread), so I use useSynchronizationContext: false (I haven’t verified that).

[UPDATED] to address the OP’s comment on how to differentiate between WebException caused by cancellation and any other error. This is how it can be done, so TaskCanceledException (derived from OperationCanceledException) will be correctly thrown upon cancellation:

public static class Extensions
{
    public static async Task<HttpWebResponse> GetResponseAsync(this HttpWebRequest request, CancellationToken ct)
    {
        using (ct.Register(() => request.Abort(), useSynchronizationContext: false))
        {
            try
            {
                var response = await request.GetResponseAsync();
                return (HttpWebResponse)response;
            }
            catch (WebException ex)
            {
                // WebException is thrown when request.Abort() is called,
                // but there may be many other reasons,
                // propagate the WebException to the caller correctly
                if (ct.IsCancellationRequested)
                {
                    // the WebException will be available as Exception.InnerException
                    throw new OperationCanceledException(ex.Message, ex, ct);
                }

                // cancellation hasn't been requested, rethrow the original WebException
                throw;
            }
        }
    }
}