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I suggest the following steps:
Between now and Monday morning, compare delivery services and pick one that can get a packet from the conference organizers to you as fast as possible. It will be a lot faster than 10 days.
Between now and Monday prepare your application.
As early as possible on Monday (UK time) contact the conference organizers. Ask whether other visa applications with just the scanned images have been approved recently.
If they say yes, send in the application immediately with the scanned letters you already have.
If they say no, ask them to send originals on Monday, using a fast delivery service. If you can, offer to pay the delivery charges. Be prepared to recommend the best service you found, unless they have a strong preference. Send in the application as soon as you receive the originals.