However, public sector union Unison, which has been campaigning for the nurseries, said the fight was not over yet.
The settings at Marylebone and Harrow had been due to close in September but were granted a temporary reprieve to give time for Unison and the nurseries' staff to draw up a business plan with a consultant.
This was presented to senior management on 30 October. But the university concluded that the plan was not viable, and last week it was announced that the nurseries would close on 31 December.
Eight nursery staff stand to lose their jobs and 40 children will be forced to find other childcare facilities.
University registrar and secretary Carole Mainstone said, 'This is a challenging time financially. We must conclude with deep regret that we cannot afford to run our nurseries - particularly as the number of students using the service is so low.
'The staff have worked hard on an alternative business plan, but we do not believe it stands a realistic chance of success.'
The university also said the business plan had called for input from the university's fundraising and marketing teams which was not practical.
The plan included a proposal to raise nursery fees by 20 to 25 per cent, which the union argued would have kept them competitive and affordable for students. Fees are currently from around £89 a week.
Unison branch secretary Barry Blinko said the union was appealing against the decision and would take the case to the University's Court of Governors at a meeting later this month.
He said that the decision to close the nurseries threatened student retention, because many student parents could be forced to abandon their studies if the nurseries closed.
Mr Blinko said, 'Closing these two nurseries will only save about £120,000 per year, but will cost student parents their education. At the same time, the college is planning to spend £1m on a new reception area. Where is the sense in that?
'Our equality impact assessment showed that these cuts are set to hit women hardest. It is vital that the college rethinks its plans.'
The nurseries have a list of more than 30 student parents who wanted to use the nursery this term, but the university stopped new parents from registering.
Interim manager of the Marylebone nursery Teresa Lorenzo said, 'The nursery could have been full. We have had lots of enquiries from students and we would have been full in September. We have a good reputation and there are also people from the local community who want to use the nursery.'
She added, 'The children who are here have settled well. Children need stability - they are not objects to be moved from one place to another.'
Christina McAnea, head of education at Unison, said, 'Many universities and colleges see nurseries as soft targets for cuts. But this is totally unacceptable. These nurseries are often the only affordable childcare options for students with young children. The closures will price many parents, especially women, out of continuing their education.'
She added, 'Unison is deeply worried about this growing trend and are campaigning hard against the cuts. The Government has worked hard to get more students from different backgrounds into university. By excluding students with children, these cuts threaten to turn back the clock to the bad old days when only the privileged few could continue their education.'
A petition to save the nurseries has been signed by nearly 1,000 people.