It's entirely up to employers. Unless they're barred by the CRB's 'Vetting & Barring ' scheme, anyone can work in childcare with absolutely no qualifications whatsoever. A private individual could (if they were mad enough to do so) employ a totally-unqualified person, with a substantial criminal record and no references, to look after their child.
For work within nurseries and other pre-school environments it's an Ofsted rule that all employees must be CRB-checked but not that all employees have any form of qualifications. (There are plenty of totally unqualified staff working in such environments).
More reputable employers will only accept staff with relevant qualifications. Most would probably not require anything beyond an HNC, so you may well not need to pursue your HND studies. But if you're seeking a career where you can later move on to managing some form of pre-school provision it might be wisest to aim for the highest qualifications available.
Chris