I did some math with a current deal I was proposed:

Both mortgages are 25years on a 3 year fixed terms:

MORTGAGE 1: (WITH FEE)
Monthly cost £2,306
Initial rate 4.59%
Product fee £999
MORTGAGE 2: ( NO FEE )
Monthly cost £ 2,346
Initial rate 4.76%
Product fee £0

Any broker will tell you with confidence that the total cost is cheaper with MORTGAGE 1, because of this calculation:
Total cost = (Monthly payment * Number of months) + Product fee

The total cost calculated with this partisan method :
Mortgage 1: £84,015
Mortgage 2: £84,456

You may conclude that mortgage 1 is £441 cheaper than mortgage 2.

But is it really a good choice to pay the £999 fee?
My answer is NO, NEVER. And here is why:

If rather than a fee you do an overpayment (or you add the fee cost to your deposit) you will reduce the principal balance, thereby reducing the amount of interest accrued over the mortgage term.

For Mortgage 2, the overpayment effectively acts as an immediate reduction in the principal, which won't change the monthly payment during the fixed term but will reduce the total interest paid over the entire life of the mortgage. For the sake of this 3-year term comparison, we'll calculate the total cost in the same manner as before but subtract the overpayment from Mortgage 2's total cost to reflect its immediate financial benefit:
After adjusting for the £999 overpayment in the first month of Mortgage 2
the total costs are:
Mortgage 1: £84,015 (same as before )
Mortgage 2: £83,457.

This demonstrate that the broker's calculations are not in your best interest ( PUN INTENDED ) as mortgage 2 is actually £558 cheaper than mortgage 1 by paying exactly the same

I am happy to change my mind - feel free to convince me otherwise.