NO, a tenant only needs to submit a claim form to the Tribunal.
The legislation that allows for a Rent Repayment Order maybe found at sections 41 and 42 of the Housing and Planning Act 2016:
41 Application for rent repayment order
(1)A tenant or a local housing authority may apply to the First-tier Tribunal for a rent repayment order against a person who has committed an offence to which this Chapter applies.
(2)A tenant may apply for a rent repayment order only if —
(a)the offence relates to housing that, at the time of the offence, was let to the tenant, and
(b)the offence was committed in the period of 12 months ending with the day on which the application is made.
(3)A local housing authority may apply for a rent repayment order only if—
(a)the offence relates to housing in the authority's area, and
(b)the authority has complied with section 42.
(4)In deciding whether to apply for a rent repayment order a local housing authority must have regard to any guidance given by the Secretary of State.
42 Notice of intended proceedings
(1)Before applying for a rent repayment order a local housing authority must give the landlord a notice of intended proceedings.
(2)A notice of intended proceedings must—
(a)inform the landlord that the authority is proposing to apply for a rent repayment order and explain why,
(b)state the amount that the authority seeks to recover, and
(c)invite the landlord to make representations within a period specified in the notice of not less than 28 days (“the notice period”).
(3)The authority must consider any representations made during the notice period.
(4)The authority must wait until the notice period has ended before applying for a rent repayment order.
(5)A notice of intended proceedings may not be given after the end of the period of 12 months beginning with the day on which the landlord committed the offence to which it relates.
Note that s.42 makes no mention of a statutory requirement on the tenant to provide a Notice. This is clarified at para 4.2 of the Guidance for Local Housing Authorities referred to at section 41(4) above:
4.2 Does a tenant have to go through the same procedure as a local housing authority if they want to apply for a rent repayment order?
No. A tenant does not have to go through the same process. To make an application for a rent repayment order, a tenant only needs to submit a claim to the First-tier Tribunal which sets out the reasons for the claim and the dates to which it relates