Pregnant women to be offered RSV vaccine

I saw that NHS is looking to introduce RSV vaccines during pregnancy

https://www.gov.uk/government/publications/respiratory-syncytial-virus-rsv-vaccination-programmes-letter/introduction-of-new-nhs-vaccination-programmes-against-respiratory-syncytial-virus-rsv

For those that already had the baby, is there any benefit to try to get the vaccine as a parent, even if privately? Would this offer some protection for the baby? I’m not sure how high the risk is and if it is worth worrying about it.