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I am not too familiar with auctions, but have looked into some elsewhere and buyers premium is usually around 30% of the sale price, plus VAT.
There is usually a sellers premium too, so the auction house gets a cut from both sides.
Not heard of 2 premiums to the same buyer though, but I am not experienced enough to say whether you are right or not.
Edit: online premiums are usually around 1% as one fee and then 20-30% on the hammer price as well.
And then VAT on top for everything.E.G. hammer price of £800
(maybe 20% VAT - £160)
1% online premium - £8
(VAT - £1.60)
25% buyers premium - £200
(VAT - £40)Total - £1209.60
Possibly with VAT too