Can the Opponent ask for costs from me if I withdraw my Trade Mark Application after the Notice of Opposition is filed?

Yes, he can ask the Registrar for such costs. However, the Registrar, in deciding whether to award costs in favour of the Opponent, will consider whether the opposition might have been avoided if the Opponent had given the Applicant reasonable notice before the notice of opposition was filed.

The Registrar is more likely to award the Opponent such costs if it had requested you to withdraw your Trade Mark Application (and you did not do so) before filing its notice of opposition. [R40] [Fourth schedule of the Trade Marks Rules]