Claiming tax relief on one-off pension contributions - impact on child benefit

I will be paying into a salary sacrifice pension when I start my new PAYE job, for which I will receive 40% tax relief. This will bring my actual salary down to £73,600. I have two children and currently receive child benefits. In order to not lose this I am considering using ISA savings to make a one-off payment of £13,600 into a SIPP. My understanding is the SIPP will automatically claim 20% tax relief on my behalf. I would then want to claim the additional 20% tax relief on that £13,600, which the HMRC website says can be done via self-assessment, but up to a limit of £10,000. How can I claim back tax relief on the additional £3,600, do I need to write to them separately? Also, as I am not registered for self-assessment, will I be able to register in order to claim under these circumstances?

Hi,

As over £10,000 you will need to write to us. Please include evidence from your pension provider of payments made in the tax year. You will also need to confirm whether the amounts included are gross (before tax) or net (after tax).
Send your letter to:

Pay As You Earn and Self Assessment,
HM Revenue and Customs,
BX9 1AS,
United Kingdom.

Thank you.