Birds nesting in chimney in October

I have had birds nesting in my chimney since I moved into this old house in April. I don't know which type of birds. I had been advised that they will leave after nesting season but it's now 14th October and they are still here. Is this usual?  I am getting cold and want to get the chimney swept so I can light a fire but of course I don't want to (and am not legally allowed to) endanger the birds!  Any suggestions please?