What is the official Catholic position on heterosexual civil partnerships?

All sexual relationships between any people not married to each other are a sin.

Furthermore,

Can. 1057 §2. Matrimonial consent is an act of the will by which a man and a woman mutually give and accept each other through an irrevocable covenant in order to establish marriage.

Since you describe your union as a "civil partnership," one concludes that you and the woman have not consented to form a marriage.

First question: is a "civil partnership" a marriage?

This seems to be a UK-specific question. This government website defines civil partnership as almost the same thing as a marriage except that it is formed by signing a document instead of saying a prescribed form of word. The question is whether you and your "partner" consider yourselves married. If so, I guess it's similar to what an American would consider a "civil marriage", where the ceremony is optional. The Church probably doesn't care much about the legal form, so you might be "civil partners" in the view of the government but actually have a church wedding.

If you are not married, then obviously it is the sin of fornication for you to have relations. Moreover, you should not be co-habiting, for obvious reasons.

If you are married, then the Church "considers" marriages between non-Catholics to be valid. This presumes no impediments (such as prior marriages and divorces).

Second question: are either of you baptized?

The Church distinguishes between "natural" marriages and "supernatural" or sacramental marriages. If you are both baptized Christians of any denomination other than Catholic, your marriage (if it is a marriage) is considered by the Church to be valid and sacramental. If you are atheists or of some other religion, your marriage is considered merely natural. By the way, if you were baptized validly, you're Christian in the view of the Catholic Church, whether you believe and practice the faith or not.

If you are Catholic, i.e. were baptized into the Catholic faith, but did not marry in church, your marriage would be invalid in the eyes of the church unless you received a dispensation to marry outside a church.

Another thorny issue is, what if one of you is Catholic (or baptized as such) but the other isn't? In that case, your partnership could not be a valid marriage in the eyes of the Church unless you received a dispensation to marry a non-Catholic and a dispensation to be married outside of a church.

Solutions

The solution to your problem is simple. If you are not married (i.e. you didn't really make "vows"), then get married and then you can enjoy all the privileges of marriage (wink, wink). If one or both of you is Catholic (or was baptized as such), then you must contact your priest or bishop about either getting married in church, or getting a dispensation to marry outside the church.

Finally, if you are Catholics but are in doubt about the validity of your marriage (i.e., if you contracted a "civil partnership" before converting to Catholicism), you can request a "convalidation" ceremony to ensure that your marriage is valid.

Relevant to your question is the fact if you are catholics yourselves.

If you are catholics, it is easy: sex outside marriage is a sin. Any civil arrangements do not make a marriage, not even if civil law calls it a marriage. You should marry “in church”.

If you are no catholics, the church is less strict and less interested I think, but still a more general rule could be formulated: there is no justification to add wrong to wrong. So, even if you are not catholic (which is not the best way, in the eyes of the church) you still shouldn’t have sex outside a lasting monogamous relationship open to children. If your relation is such, then sex in itself isn’t a sin, I think, in the eyes of the church. But it really is rather theoretical, as the Church teaches mainly for catholics.