Baroque Does 'Reception' fit the bill for what you want? Possibly not, since you've been part of the CofE for a long time already, and it seems to be designed for people just "moving" from other denominations to Anglicanism...(???).
I don't know anything about this (and hadn't heard of it before) but I remembered reading something about it on the website of the church we went to in the US. I'm C&P-ing it below, but have taken out the name of the church. (It's obviously aimed at an American audience, but it talks about "the Anglican tradition", so I am guessing it's the same here.)
"The rite of Confirmation is for individuals who wish to publicly affirm their mature Christian commitment. Reception is a public acknowledgment and welcome of a Christian person who has chosen to belong to the Anglican tradition of the Christian Church. These rites are administered by the Bishop.
People who wish to join the Episcopal Church will often ask, ?Should I be confirmed or received?? While such a question is best answered in conversation with Cathedral clergy, a general answer would be: If you have been confirmed in the Roman Catholic, Orthodox, or Lutheran traditions, it is likely that you would be received. If you have never made an adult profession of faith, it is likely that you would be considering Confirmation.
At the XXX, the most significant liturgy for Confirmations and Receptions is our Easter Vigil, celebrated the night before Easter Sunday. Our Cathecumenal Course focuses upon preparing for this yearly liturgy, as a context for Christian formation. The other service where Confirmations and Receptions takes place is during the annual visit of the Bishop to the Cathedral congregation.
If you are interested in Confirmation or Reception, please contact the Dean of the Cathedral."
Oh, right... there's the Easter Saturday thing again. So that makes sense.
Another nice thing we did over there (sorry for the rose-tinted specs, but I did have a really good experience there) was a renewal of baptism as part of the baptism service. So after the baptism of the baby, everyone who'd been baptised themselves went to the font and touched the water or crossed themselves with it as a renewal of their own baptism.