If you bought the iPhone 4 new through the Apple Store or a Cellphone store, it comes with a one year warranty, not a 90 day warranty. This applies in The UK as well as in the US.
As per the iPhone 4 warranty:
Apple warrants the Apple-branded hardware product and accessories contained in the original packaging ("Apple Product") against defects in materials and workmanship when used normally in accordance with Apple's published guidelines for a period of ONE (1) YEAR from the date of original retail purchase by the end-user purchaser ("Warranty Period"). Apple's published guidelines include but are not limited to information contained in technical specifications, user manuals and service communications.
The date of purchase is tied to the serial number at the point of sale. Your eBay purchaser will have the remaining balance of the one year warranty. They can check the status of the warranty at: https://selfsolve.apple.com/agreementWarrantyDynamic.do
In short, yes, they will have the warranty, but the warranty does not "start over" when the buy it, they only get the remaining balance.
If you have AppleCare Plus, it must be manually transfered by calling Apple's 800 number. AppleCare Plus can only be transferred ONE time. (The purchaser could not transfer it a second time)