Re: Auction ? Why not just convert to £ ?
1) 250k is nothing, daily traded volume is in hundreds millions of USD, so no worries there.
2) Selling on public exchange is a form of auction, there is a line of bids which you can fulfill. They would get circa 20% more this way as this was the auctioneer fee (crazy high btw).
At least I would find someone who will do it for 5% max, as there is a little they have to do to store or deliver the crypto assets.