Cost to Upgrade on Eurostar when checking in
 

Recently, I think I read of someone having the chance to upgrade when checking in for their Eurostar trip London-Paris.
If so, could you tell me how much more it would have been? I recall one advantage was being able to pre-book a taxi for your arrival in Paris.
We arrive in Paris On Oct 20th, the day of the final game of the Rugby World Cup. We already paid a premium for tickets on that date compared to the usual fares. Perhaps they will try to charge more for an upgrade that day too, so it would be nice to know what was offered at the check in on a non-rugby day!
Also if we could pre-arrange a taxi for that date, when taxis might be even harder to get than usual, it would be a bonus!

I've just googled through the Eurostar website and the only time you can upgrade is if you have a semi or fully flexible ticket

The question however - will there be any seats to upgrade to?