Hi i bought a pay as you go iphone 3gs in august in the uk and now my headphone slot is broken ( jack only goes 3/4 of the way in) its unlocked and running a vodafone sim only sim, so if i take my phone back to the apple shop where i bought it, will they give me another one? and also will i be able to unlock the new one?

Many thanks

It depends on whether you bought the Apple Care package. If not, you're out of the warranty period I think. If you ask nicely, they'll likely repair/replace it for you anyway...if you get the right employee. In the US, they rarely turn away someone even if out of warranty unless the phone's obviously been abused or maltreated.

Do not bring it to them unlocked or jailbroken. That lowers your chances of getting help since, officially, that violates the warranty. It's best to get it repaired. If it's replaced, you'll likely get a newer model with the new iBoot version that can't be properly jailbroken.

14 days after you are only entitled to a refurbished replacement. Apple does very little repair (some apple stores have a tool that can replace screens on site). Refurbished iPhones are usually constructed from parts obtained from returned iPhones as well as new parts where necessary. If the store has no suitable refurb phone in stock, they can give you a brand new iPhone.

Remove all visible traces of jailbreak.

The warranty is 1 year so you are still under warranty.