hey piggles,
it would tarnish your name more if you'd "pretend" to go ahead with the competition and pull out later. your current institution will then not be able to nominate anybody else and will thus lose a chance of getting a funded student. if you tell them now, they will be fine with that, as there is still time to let someone else (a runner up for example) have a go. if you "pretend" to go ahead, you are also cheating that runner up of their chance. that seems quite egoistic and unfair to me. also, your exams will be graded anonymously and the department's likes/dislikes of you should not affect your grades.
on the other hand, i think you should try every chance to get funding. ESRC open competition is very competitive, it is not very likely that you will win funding. next year neither. so if you pull out now and then next year don't get it, your unfunded. that's quite a risk.