Here, here, Checkboard.
Single engine taxi at out LHR saves on average about 80kg per time which with fuel prices as they are is not to be sneezed at. It adds 2 more short checklists to the normal proceedure but I wouldn't say that it complicates things much. You don't get out of sequence because it is built into the SOP. As far as line up clearances go ATC at LHR are extremely helpful when they know we are single engine. In any case most crews err on the side of caution, timewise, taking the view fuel saved up to second engine start is a bonus rather than fuel wasted after start being wasted.
In answer to Nubboy's query we did single engine taxi in on the 737 but not taxi out. I suspect the only reason was to be different to th DC9!