Pedantic point: Anything which involves data coming down your phone line (or however else you access the internet) is 'downloading'. It doesn't matter whether you're accessing a page here on AB, checking your emails or streaming audio or video content; it's all 'downloading'.
The BBC website says that an hour long programme on iPlayer uses 225 MB of data:
https://www.bbc.co.uk/iplayer/help/how-to-guides/getting-started/3g_4g
So your two hours of viewing would use nearly half a Gigabyte.
However other sites suggest that the actual amount of data used might be considerably higher than that. This site, for example, suggests that (even if you select the low bandwidth' option) BBC iPlayer actually uses 450 to 500 MB per hour
http://travelforlesss.blogspot.com/2012/03/will-10gb-be-enough-for-my-iplayer.html
so your two hours of viewing time could use close to a Gigabyte of data.
That site also points out that watching in HD can push the usage up to around 650 Mb/hour (meaning that you'd use 1.3 GB in two hours). This site seems to broadly concur with that figure:
http://mobilenetworkcomparison.org.uk/how-much-bandwidth-does-iplayer-use/
Other video streaming sites might use data at a faster, or slower, rate, depending upon the quality of the stream.