No, Madonna, I don't think you have to promise anything particular in a civil service other. The statutory words (appended) don't specify at all what marriage is.
All civil marriage ceremonies and religious ceremonies other than Church of England, Jewish or Quaker, must incorporate statutory declaratory and contracting statements, to be said by both of you, for your marriage to be lawful. The registrar will usually suggest that the following traditional statements are used:
Declaratory Words
I do solemnly declare that I know not of any lawful
impediment why I, [your full name], may not be
joined in matrimony to [your partner's full name].
Contracting Words
I call upon these persons here present to witness that I,
[your full name], do take thee, [your partner's full name],
to be my lawful wedded wife [or husband].
However, since February 1997, you may choose to use either of the following alternative declaratory and contracting words:
Alternative Declaratory Words
I declare that I know of no legal reason
why I, [your full name], may not be joined
in marriage to [your partner's full name].
or
by replying 'I am' to the question
'Are you, [your full name], free lawfully
to marry [your partner's full name]'.
Alternative Contracting Words
I, [your full name], take you, [your partner's full name],
to be my wedded wife [or husband].
or
I, [your full name], take thee, [your partner's full name],
to be my wedded wife [or husband].