In exporting from MP4 to a 4minute full HD H.264 Quick Time file what sort of file size would you say was reasonable ?

If both were h.264 and you used pass through then the same size. Mp4s are generally h.264 encoded already (not always though)

I am exporting from the Premiere CS5 timeline. 'From MP4' was misleading ( the footage is MP4. ) So no, the source is not H.264. My 4 mins HD Quicktime H.264 output file is 885 MB. Should I lower the Bitrate Settings data rate ?

That seems like you are making a full resolution h.264 file which is good for cinematic distribution by internet or for playing on a broadcast server but it might not be what you want. You certainly should look into throttling the bit rate depending on the ultimate destination of your export. Since I am not familiar with the export options of Premier, you should see if there are some presets for YouTube or broadband internet.

Thanks William. It is for broadcast and the Production Manager has just emailed me to say that the file size is no problem - I wanted to check that that was the case before send it to him. That's why I asked this question on the forum but I ran out of time and had to post it off. Problems arise when editing on Premiere for a production facility using FCP.