Is there a legally mandated filing fee and/or deposit?

Electoral Act 1968, 138

Cost of petition

All costs, charges and expenses and incidentals to the presentation of an election petition and to the proceedings consequent thereon shall, subject to paragraph (j) of section121 be defrayed by the parties to the petition in such manner and in such proportions as the High Court may determine, regard being had to the disallowance of any costs, charges or expenses which may, in the opinion of the Court, have been caused by vexatious conduct, unfounded allegations or unfounded objections on the part either of the petitioner or the respondent, and regard being had also to the discouragement of any needless expense by throwing the burden of defraying the same on the parties by whom it has been caused, whether such parties are or are not on the whole successful.

(2) Costs may be taxed and recovered in the same manner as the costs of civil proceedings in the High Court.

http://aceproject.org/regions-en/eisa/BW/Electoral%20Act%201968.pdf