Getting time out exception using webclient downloaddata method to download images from URL while I hit URL from browser easy to get download

This isn't a question we can answer: it's down to you and the site you are accessing.
We don't know how busy the site is, how much data is being transferred, how long it takes. We don't know what the site does with repeated requests: some may deliberately delay responses to mitigate possible DDOS attacks.

So start by making notes on the URL's you are requesting, and try accessing them manually via a browser. How fast are they being served? How much data is being transferred? What happens if you start several of them in quick succession? Does anything change?

It may be that you need to extend timeouts, it may be that you need to slow the frequency at which you access the site - we can't tell. And possibly, contact the site admin and see what he says.

So start by gathering information - we can't do that for you!