I would have thought that your Agent should have told you that the costs were your responsibility at the same time that he told you to contact an electrician. So my guess is that as the account has come in higher than the Agent anticipated, and as they don't think that the Landlord will be happy with the expense, they're simply attempting to off-load the responsibility for payment to you.
The electrician's invoice would (I assume) have been sent to the Agent, so in consideration of that and the other circumstances, I'd refuse payment.