Hey simon from UK welcome to Qatar.

For what I know the most likely place for brits and irish is the Irish Harp in Sheraton Hotel.

On the other hand near Al Saad you could probably give it a try in Orion or The Qube in Ramada Hotel.

You can also try

http://www.qatarliving.com/group/qatar-scottish

http://www.qatarliving.com/group/the-british-club-in-qatar

Best of luck!!!!