Hi,
If you have no bids on the item you can revise the listing and change the start price to that agreed and once they have bid 'end the listing early to sell to the highest bidder':
http://pages.ebay.co.uk/help/sell/end_early.html
If you revise and add a BIN price then it has to be a minimum of 40% higher than auction start price. You'll also need to have them on standby to buy in case someone else jumps in.
If you have bids, then it would be unfair on existing bidders to cancel and relist.
Those who ask for a BIN are usually hoping for a bargain. As most bids are placed in the last few minutes of an auction, it's often best to let it run and invite the person to bid.

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