Initial response is that you cannot use an email decision to authorise a project. The Chair will need to call an Extraordinary Meeting giving a week's notice.
However..... depending on the cost implication of the decision that needs to be made, there may be cover under delegated spending powers of the Clerk / Proper Officer. If an urgent decision to spend money is considered business critical, then your Financial Regulations may allow for a spend eg, if urgent tree works were required for the safety of the public...