Both you and the mother have the same parental responsibility, and she should not be preventing contact due to COVID unless she is self isolating due to symptoms.
Because there is no court order in place, there is nothing for you to enforce in court. If the children are still going to school, there is no reason why you cannot collect and drop off the children there, as you have as much right as she does to have the children in your care.
That said, if she is going to be difficult and prevent contact, your next option is to try mediation, which is a requirement before you can put in an application to court. I suspect mediation won't work, or she won't engage, in which case the mediator will be able to sign off on your C100 application to the court for a child arrangements order.
The court will list the matter for a hearing, and both of you will be contacted by CAFCASS to discuss the issues and CAFCASS will do background checks and write a safeguarding letter to the court with recommendations on what to do next. At the first hearing both of you will be able to give your views, and if an agreement can be reached an order can be made that day - if not, interim orders can be made and directions for further investigations, e.g. a s7 welfare report so that the children can be spoken to.
None of this will happen overnight - it will be at least 5-6 weeks before a hearing is listed, so start the process as soon as you can. In the meantime it may be worthwhile telling the mother that you have the exact same rights as she does and that her stopping contact is unreasonable.