When my eldest was baptised, I wanted to ask a very old friend of mine to be godmother but knew she wasn't baptised herself (my mother was surprised when I told her though). I discussed it with our vicar and, as we were regular attendees and had two other godparents he was happy to involve her in the service. As he put it, part of the responsibility of godparents is to help ensure the child is brought up in the Christian faith, and he could trust that we were going to be doing that with or without help.
What to do in your position will depend a lot on your own "faith status" - there are non-CofE churches with varying definitions and procedures for determining who is a "full member" of the church and I would expect most CofE vicars to be happy with any Christian person being a godparent in the fullest sense. So if you consider you are Christian, proceed accordingly and maybe discuss with their minister beforehand or a leader within your own church if relevant.
If you are being asked by a family who are fairly nominal churchgoers, then I guess it is between you and them first, but may need to be discussed with the minister depending on their approach. Children are one of the "life points" that brings people into the church!
Finally, as a relative you will be involved in this child's life anyway, so if it turns out that there is reluctance to have you as an official godparent - or if, when you look into the promises you are asked to make as part of baptism, you yourself are reluctant - then actually it really doesn't matter.