Enjoying water 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 in a swimming pool, 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 come to a swimming pool 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/her to a pool. NHS Guidelines can be found here.