Only same-sex couples are currently eligible for civil partnership by law.
Heterosexual couple Rebecca Steinfeld and Charles Keidan challenged the law and lost - but the ruling shows the matter is far from resolved.
A heterosexual couple have lost a High Court challenge against a bar to them entering a civil partnership.
More than 60,000 civil partnerships have been formed in the UK since the legislation was introduced in 2005.
The number of civil partnerships rose by 3.6 per cent to 7,037 in the UK last year, figures from the Office for National Statistics show.
There were 7,037 #civilpartnerships in the UK in 2012, up 3.6% since 2011 http://t.co/cZz6GOUrle
The average age of men forming a civil partnership in 2012 was 40, while for women the average age was 37.6.
The number of civil partnership dissolutions granted in England and Wales in 2012 also rose by 20 per cent.
The figures have been released after legislation introducing same-sex marriages in England and Wales received royal assent from the Queen in July, in spite of opposition from many Conservative backbenchers and religious groups.