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What does your contract with the airline say about that?

What does your contract with booking.com say about it?

Aside from the terms of whatever contract(s) you entered into regarding the flight, the missing piece of the story seems to be the timings. You mentioned that if you are not purchasing a reserved seat, online check-in opens 3 hours before departure. You then mention that you arrived at the airport 2 hours 55 mins before your flight and went to the desk to check in - did you make any attempt to check-in online within 3 hours of the departure, or did you just go straight to the desk?

(I can't see any particular peril in telling us which airline is involved)

Where can I find my contract with booking.com

It would probably have been made available at some point during the booking process, and/or in any subsequent communications from booking.com and/or any other involved party.

I've just run a dummy search on booking.com and at the point I was asked to make payment I was presented with a number of terms & conditions that I would be agreeing to:

I found this on booking .com website terms and conditions

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I shared what I could find in their terms and conditions
Because i couldn’t find any contract with them

I've booked numerous  flights with Ryanair, easyjet and BA.
I've never been asked to book a seat when checking in.
it seems odd as when you book the flight you either do or do not book a seat.

It is likely to be difficult to offer much advice unless/until you can find copies of the contract(s) you entered into, either with the airline or any intermediary such as booking.com

I've never used booking.com to book flights, but whenever I have booked flights, the confirmation email(s) I have received have provided the terms and conditions, either directly or via a link.

I have found the summary of the terms and conditions which booking.com sent by email but i can’t see anything about payment for check in at the airport
But the email they sent me for check in said “check is now open, and if you don’t check in online you maybe charged