I travel between EDI-DOH-BKK every 17 days or so and have done this for around 12 months now so have a little insight to the whole upgrade offers that come through. As Florin mentioned you can check on the mybooking section which will show the current price for an upgrade.
If you haven't already, download the app and log in/ sign up to the rewards program. Your upcoming flights will then be shown on the homepage and have something like "your flight QRXXX departs in X days". Below this it usually offers you to add extra luggage and save up to 70% which you can swipe down and if an offer is available it will pop up here. An email sometimes comes through also but this is not always the case and the upgrade offer can be shown in the app without receiving an email.

As for price I have never seen a single leg of the journey offered for less that £500. This is obviously still cheaper that your quote from the travel agent and also typically depends on the flight/config. Q-Suite upgrades are more expensive.
In general the upgrades have been around 600-1000 per leg.