rewrite - help needed

If you redirect the user to abc.co.uk, the browser will update to reflect that.

If you want the address bar to stay def.co.uk, you can't redirect the user. Rather, you'd need to do the redirection locally. For example:

when HTTP_REQUEST {
    if { [string tolower [HTTP::host]] equals "def.co.uk" } {
         change the Host header on the way to the server (as needed)
        HTTP::host "abc.co.uk"

         send to the def.co.uk pool
        pool def_pool

         if the URI is empty, redirect to /app/login
        if { [HTTP::uri] equals "/" } {
             sends a relative 302 redirect to the user
            HTTP::redirect "/app/login"
        }
    }
}