Is it due a timing belt replacement?.

If it isn't, then I wouldn't bother with it.

If it is due, not replacing it will affect the value, though I've no idea if that would be by more than the cost of replacing it.

Hi I have a 2013 Ford Fiesta that I am thinking about part exchanging. At my last service the garage recommended replacing the timing belt for £350. Is it worth me doing this before getting rid of the car?

If you were selling privately, then yes. If part-exing, probably not, because the allowance you will get will probably assume that the cambelt will not have been changed. Why would you trade in a car just after investing £350 in it ? :-)