In more relaxed times, before austerity, it wasn't unusual for the Mayor's Allowance to be handed over to the mayor to do as they wished. One use for the council on which I sit used to be a Civic Dinner, to which a variety of local dignitaries were invited. It was a congenial event. Other uses included the costs of attending events in the role of mayor.
This approach was abandoned some time ago, and now the Mayor's allowance is simply a ceiling on the actual out of pocket expenses the mayor is permitted to claim. But that is one particular council's choice, in part a reaction to concerns over citizens' ability to shoulder the burden of council tax in hard times. On the whole, our view is that it isn't the council's job to take tax money and hand it over to charities except where there is a specific benefit to the citizens of the parish that might not be obtained without the council's help.
Either approach is lawful provided it is clear that the mayor is not making council decisions, but is simply putting into practice arrangements decided by the council.