This is something that there has been some work on.  I would first want to know what the reasons for low uptake are.  Could you perform a focus group or series of individual qualitative interviews to identify concerns? These are commonly cost, low perceived necessity and/or high perceived risk associated with vaccination, and anticipated regret if child is vaccinated.   If there have been cases recently of children having negative reactions to vaccines this needs to be considered.  Vaccination risk perceptions can be unduly influenced by availability bias.  Some references from our group you find of help are given below. The will point you to other related work :

Wang LDL, Lam WWT, Wu JT, Liao QY, Fielding R. Chinese immigrant parents' vaccination decision making for children: a qualitative analysis. BMC Public Health. 2014, 14:133. DOI: 10.1186/1471-2458-14-133

Wang DL, Lam WWT, Fielding R. Hong Kong Chinese parental attitudes towards vaccination and associated socio-economic disparities. Vaccine 2016, 34, 12, 1426-1429

Wang LDL, Lam WWT, Wu J, Fielding R. Hong Kong Chinese women’s lay beliefs about cervical cancer causation and prevention. Asia Pacific Journal of Cancer Prevention, 2014, 15, 18. DOI:http://dx.doi.org/10.7314/APJCP.2014.15.18.7679

Wang LDL, Lam WWT, Wu JT, Liao QY, Fielding R. Chinese New Immigrant Mothers' perceptions about adult-onset non-communicable diseases prevention during childhood. Health Promotion International (2014) May 29th. Doi:10.1093/heapro/dau029

Liao QY, Cowling BJ, Lam WWT, Ng DMW, Fielding R. Anxiety, worry and cognitive risk estimate in relation to protective behaviors during the 2009 influenza A/H1N1 pandemic in Hong Kong: ten cross-sectional surveys. BMC Infectious Diseases. 2014, 14:169. DOI: 10.1186/1471-2334-14-169

Liao QY, Wong WS, Fielding R. How do anticipated worry and regret predict seasonal influenza vaccination uptake among Chinese adults? Vaccine (2013) published online, 29th July, doi: 10.1016/j.vaccine.2013.07.009

The first place to start is to find out why this has happened. A block rejection is more likely due to some misunderstanding/wrong perception of the risks and/or benefits of the vaccine. Some qualitative examination-individual or group discussions in collaboration with a social scientist will help.

In addition, remember to observe delivery of vaccines at the service points in the area, interview healthcare providers for their perspectives e.g. stock outs, etc. It is important to ask about observed adverse events following immunization- deaths, abscesses, etc. These are likely causes of a block refusal like you have observed. 

Following on from the above, likely interventions can be identified and implemented.

You may find this review useful.

http://www.dx.doi.org/10.1002/14651858.CD008145.pub3

Also look at work by Julie Leask http://bmcpediatr.biomedcentral.com/articles/10.1186/1471-2431-12-154 she's done quite a bit of work in finding out why people don't vaccinate (often related to access to services) and how to improve or promote vaccination, she's active on twitter and other social networks @JulieLeask