How can I help feed bluetit chicks?

Hello all,

We have a camera bird box that has been used over the last 4 years to successfully hatch clutches of bluetit eggs. A female laid 10 eggs this year which all hatched last Saturday 1st May, more or less exactly the same date as previous years. However, the parents appear to be struggling to find sufficient caterpillars to feed their young and all but three have now died. The oak tree at the bottom of our garden has in previous years been a source of caterpillars, but with the cold Spring it is 2-3 behind where it usually is and the leaves are only just opening. We have feeders with seed and dried mealworms and suet log feeders in the garden for the adult birds. Is there anything we can do to help the parents feed the survivers through to fledging?