Welcome to the forum. You're entitled to prior notification of the amount of an upcoming direct debit if it's different to the previous one; you're also entitled to an explanation of why you've been charged for the callout.
I'd dispute the charge and ask for an explanation. Meanwhile, if it helps, the Direct Debit Guarantee also gives you the right to tell your bank that the payment was incorrect; they are then obliged to replace the funds and sort it out with BT.
Welcome to the community forum. BT Should as @pottyperson has said, given prior notification of the amount before the Direct Debit was taken. As well as this BT should have let you know of the potential charge at the time of the engineers visit being booked.
If you take a look at Engineer charges it explains under what circumstances charges would apply. When you spoke to BT did they explain why the charges have been raised?
I do understand that £129.99 is a lot of money and more so at this time of year. I'll be able to take a look at your account to see why that charge has been applied.
Please can you send me in your details using the "Contact The Mods" link found in my profile?
Just for information, the engineer is not able to say if the work is chargeable. He just submits his work sheet and the paper pushers decide if it should be charged for or not.
I would do as pottyperson has suggested although that won't help your cash flow mean time.
EDIT: Post overlaped with the moderator's post. I would suggest you contact them as I'm sure if they can they will help sort this out.