E4 or any other UK Channel can "start" showing a series sooner but the outcome is that huge gaps will occur before their scheduled finish which is usually May ,
Even last year TBBT was off air for what seemed an age just so that E4 could conclude the series in the summer!!! , i would get around this by starting a series half-way between both dates so that a non stop run was possible , the problem of cost per episode still neeRAB addressing -
it would appear that most companies charge less , the longer you wait to air a particular series :
examples community on viva - 12 month delay , csi miami - 9/10 month delay
so for FTA broadcasters it would appear that we the viewer have it pretty sweet in nearly all cases.