In the Catholic Church (as I assume the C of E) we believe in ONE baptism. So as long as it had the right form and the baby/individual was baptised "In the name of the Father, the Son and the Holy Spirit" then it is a valid baptism. So Christian baptisms who use this form of baptism (Baptists, Pentacostals, Lutherans, C of E etc) can all become Catholics and do not need to be "re-baptised".
However, people from a faith such as Mormonism that talk about Jesus but who do not believe in the Trinity and don't actually have the same understanding of Jesus as Christians, would need a Christian baptism.
Your baptism is recorded and you can therefore get evidence that you have been baptised when you are ready and desire to have the other sacraments of the Church (First Holy Communion, Reconciliation, Confirmation, Marriage etc.).
If there is no evidence of your baptism (no records, no witnesses etc) you can receive a Conditional Baptism as a Catholic which means the Church is Baptizing you because we are not sure if you ever received a Christian baptism previously.
Baptism is a Sacrament and entry into the Church in Catholic theology so it is taken seriously.