Swimming is the one thing a baby can do at any time! No need to wait!
New Mums should wait about six weeks before they go swimming, just to make sure that they have recovered well. If they had a caesarean section or a perineal tear, it may be recommended that they wait longer than six weeks. Check with your GP.
However, your baby can go swimming at any time from birth. If you want to take your baby straight away, its a good chance for your a partner or a carer to take your baby. There’s no need to wait until your baby is immunised before taking him to a pool. NHS Guidelines can be found here.