If there are no amendments to the standard text then the Contractor is not obliged to submit an application for payment. The obligation is for the PM to make an assessment of the amount due at each assessment date and certify accordingly.
If Option W1 applies, which it could within the UK for a project which does not fall under the definition of a ‘construction contract’ under s104 of the Construction Act, you could refer the matter to the Adjudicator due to the PM ‘not having taken an action’. You are entitled to interest under clause 51 for a late payment, although this doesn’t necessarily help with cashflow issues.
A better solution might be to remind the PM that they have not complied with their obligation to certify payment, especially at such an early stage of the project.