Webpage access with other methods ?

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C#

I have this new class "WebPage". I am calling it from a button event in Form1.
The problem is that I Re-Call this entire process of website identification every time I go to a new page on that website. I think this BIG method is needed only one time, when I first access the website. My intuition say that I should use something else than this big code for each other pages on the same website. I am wrong and I should stick with what I have and working already? Or I am right and there are other methods (After) this one ?
Thank you !

public class WebPage
{

    public string GetText(string url)
    {
        //Special webpage Reading (extract info from page)
        HttpWebRequest request;
        HttpWebResponse response = null;
        Stream stream = null;
        request = (HttpWebRequest)WebRequest.Create(url);
        request.UserAgent = "Foo";
        request.Accept = "*/*";
        response = (HttpWebResponse)request.GetResponse();
        stream = response.GetResponseStream();

        StreamReader sr = new StreamReader(stream, System.Text.Encoding.Default);
        string text = sr.ReadToEnd();
        if (stream != null) stream.Close();
        if (response != null) response.Close();
        return text;
    }
}

What I have tried:

the code I put in already