booked the incorrect dates for airlines flight

I recently booked two return British Airways flights from Gatwick to Bordeaux so my wife and I could join my daughter on holiday there next summer. Immediately afterwards, my wife discovered we had booked the wrong dates.
The error was entirely ours. I logged back into the BA site and found I could change the flight dates to depart a week later using the booking manager. The times, flight numbers and prices were identical to the original ones but there was a fee of £120 to make the changes.
I thought this was a bit steep, but better than having to book new flights, so I went ahead. As I did so, a confirmation email came through for the original flights. This said: “Please check the details of the items purchased are correct. If you have made a mistake, you may cancel your flight booking and claim a refund without penalty, up to 24 hours from when you made the original booking. Refunds under these circumstances can only be requested by calling our contact centres.”
I phoned the call centre and explained what had happened. The agent said that as I had changed the flight details myself I was deemed to have accepted the flights and therefore she couldn’t cancel them for a refund. I said I was happy with the revised flights and didn’t want a refund, only a waiver of the £120 change fee. This request has fallen on deaf ears at BA. Is this fair?
Gill Charlton, consumer expert, replies
Like you, I didn’t realise that you could amend or cancel BA flights without penalty within 24 hours of making the reservation. It’s good to see an airline recognising that customers should not be penalised for making genuine mistakes in online reservations.
Unfortunately, in your rush to rectify your mistake, you made the amendments via the website and accepted the change fee, thus giving up your right to take advantage of the cooling-off period.
BA says that to make changes free of charge customers must telephone a contact centre. However, as a goodwill gesture, it is refunding the £120 fee.
The airline says that the 24-hour cooling-off period also applies to flights sold through agents. However, some agents have different timescales for amendments, requiring notification by the end of the business day; others refuse to allow any changes or cancellations once payment has been taken.
While most amendments must be made within 24 hours, an exception is made for those getting married and later realising they have booked flights in different names from those in their passports. In such cases, BA does not charge for the name change, though it will ask for documentary evidence.