This might seem obvious but if you are able to, the first step should always be to discuss the matter directly with the other parent to try to establish the reasons for their objection. Hearing each other's points of view can be very useful, and you might be able to alleviate the other parent's concerns or they might highlight something that you had not thought about. You might even be able to reach a compromise, eg perhaps you agree to wait until the child is a certain age, at secondary school, there is further government guidance, etc.
Not only can it be quicker, more cost efficient and less stressful to reach an agreement between you, it is positive for your child to see their parents working together even if you are parenting apart.
Whilst is always preferable to keep matters out of the court arena, sometimes this is not possible. If you aren't able to reach a compromise and agree on the matter then either parent has the option to make an application to the court. The welfare of the child will be the court's paramount consideration.
In the 2020 case of M v H, the court granted a parent's application for a specific issue order requiring the parties’ children to be given routine childhood vaccinations. The decision related to vaccines currently on the NHS vaccination schedule and the court was satisfied that it was in the children’s best interests to be vaccinated. In summary, the court found:
Although this case relates to routine childhood vaccinations, the court confirmed in passing that, provided the COVID-19 vaccination is approved for use in children, the court is likely to consider such vaccination in a child’s best interests.
As the UK regulator has now approved the use of the Pfizer-BioNTech vaccine in children aged 12 - 15 it is likely that the court would rule in favour of a child this age being administered the vaccine. We are yet to see if the vaccine will be recommended for children below the age of 12, however it is likely if this is approved, the courts would also consider such vaccination to be in a child’s best interests.
It is very likely that unless there are exceptional circumstances, the court's ruling on this matter will mirror the advice in the NHS vaccination schedule.