Can't promise, but here's a start:

This is not the traditional form of words in England. Pepys refers I think to ‘coffee house’ and ‘coffee club’, not ‘coffee room’.
http://www.pepysdiary.com/archive/1661/05/27/index.php
http://www.pepysdiary.com/archive/1660/01/20/index.php

Hogarth pictured the scene:

http://www.shu.ac.uk/schools/cs/teaching/sle/Gallery/Hogarth/HogMidConv.htm

Another common description is ‘coffee shop’. The first one?
“It started out in 1652 as the Turk's Head, a common-or-garden tavern of its day serving wine and ale under the watchful eye of landlord Edwards. However, Mr Edwards didn't realise that he was setting the foundations of a little piece of history when he returned from a journey over seas loaded with coffee beans and accompanied by a surf named Pasqua Rosee (Easter Rose) who was adept in the art of soaking the beans to produce a palatable beverage. Setting Pasqua to work, Edwards invited his friends to call and sample the new drink. Within days the word spread from one side of the City to the other and soon Mr Edwards was tearing his hair out through interruptions from a constant flow of visitors. He was at his wits end when the bright lad suggested he might consider charging for the infusion. Brilliant idea - Edwards leapt in the air, instantly made enemies of all his friends, and the very next day the first coffee shop was born.”
http://www.geocities.com/TheTropics/Cabana/9424/page25.html#Salisbury

Around 1700 ‘coffee room’ was clearly known:
http://www.travelpublishing.co.uk/CountryLivingSouth/Wiltshire/CSO26061.htm

Nowadays I think it’s rarer in ordinary use, and would tend to have the connotation of something like a staff canteen, community meeting centre or private club facility. Some of course are slightly grander than others ;)
http://www.carltonclub.co.uk/facilitcoffeeroom.htm

And some are marked by true British eccentricity:
“Coffee is not served in the Coffee Room…”!
http://www.oxfordandcambridgeclub.co.uk/facilities-dining.html