As a resident of E1W, St Katharines by the Tower, I have asked the same question and indeed requested that the webmaster of SE1 extends across the river to include us! We need someone here with the same dedication to set one up!
I too find the SE1 site a great source of information, there is a real community there that sadly does not seem to exist on this side of the river. Too many people here are new to the area, while property is used as 'pied a terres' or suffers from the 'investment blight'. Our other problem is that many pubs and restaurants follow City opening times, i.e. not open at weekends, although things are improving.
As a result, rain or shine, I am frequently seen plodding over Tower Bridge to enjoy the delights of SE1!