One in seven (14%) are hoping to either start or extend their family in the next few years.
Of these, two-thirds (67%) reveal that financial considerations do play a role in when they will decide to have kids; with more than one in five (22%) claiming money has been key to their thinking.
Of the people who admit that finances do have an influence on when they will start or grow their family, one in three (35%) say they are trying to pay off their debts first.
Depending on the amount of debt, this could take time but may also put them in a better position to apply for credit in the future, such as a mortgage for a bigger home.
With this in mind, one in five (21%) respondents who say their money matters have influenced their family plans also reveal they are saving to move into somewhere larger before they start planning for a baby.
And two-fifths (45%) say they have started to save up so they have a nest egg in place when they have children.
Women are keener to move to a bigger place than men, according to the research.
A quarter (23%) of female respondents who say their finances play a part in their decision to start a family reveal they are doing this, compared to fewer than one in five (18%) male respondents.
According to the Office for National Statistics, the average age of UK mums last year was 30.
Respondents aged between 25 and 34 years old, who the research reveals are the most inclined to be thinking of starting a family in the next few years (36%), are among the most likely to be taking steps to pay off their debts first.
More than a third (38%) of respondents in this age group say they are doing this, while 44% are saving up.
Ian Williams, spokesman for DAC, said: “Starting a family is a big life step and can be expensive, so it’s perhaps no wonder so many people say that their finances do play a role in when they think they’ll have more kids.
“Saving up for a rainy day or putting money aside to pay for a larger home are all natural instincts when preparing for parenthood.
“Paying off debts is also sensible, although it’s surprising to see that so many people are having to take this step.
“Anyone keen to start a family who feels that they have a long time to wait because of the level of debt they’re in may want to seek professional debt support and advice to see if there’s a way they can get back in control of their finances sooner.”