Yes, a non-availability of birth certificate can be accepted for a UK student visa application. When you don't have a birth certificate, providing a non-availability certificate is the appropriate alternative to demonstrate that you have made efforts to obtain the birth certificate but it is unavailable.
However, it's important to note that immigration regulations and requirements may vary over time, and it's always advisable to double-check the latest guidelines provided by the UK Visas and Immigration (UKVI) or consult with an immigration advisor for the most accurate information regarding your specific situation.
Ensure that the non-availability of birth certificate is duly issued by the appropriate authority and meets the requirements specified by the UKVI for visa application purposes. Providing additional supporting documents, if available, to substantiate your identity and birth details can further strengthen your visa application.