"Dear Ms Bloggs. I would like to apologise for the confusion regarding the wording of your contract, specifically the salary figure which is incorrectly stated as £15000 when It should read £13000 which is what it said on the offer of employment. I do apologise....................................etc., etc.,

And that is that!

It is accepted that people make mistakes. As for losing money? I don't quite understand as she knew it was £13,000 when she was offered the job wasn't she?

"....and please find attached the corrected page of the contract"

In reply to David Perry:

Yes my argument was the offer was correct and we have been paying her the correct amount but it is a human error on the contract. She says she is losing out as she has given up some work outside of this role based on the figure on her contract

In reply to Andrea Jennings:

Well you formed a contract and then amended that contract to include remuneration at an increased level, with the offer, acceptance, consideration etc, whether or not it was intended. However, I'd suggest the most she could argue is that you pay her at the higher level for the period of notice in her contract - in the ultimate scenario that you dismiss and re-employ.

As said, mistakes do happen, and it's really frustrating when it happens in this kind of situation. I did the same thing a few weeks ago, giving the wrong hours in an offer letter. Most new employees recognise (as mine did) that arguing about a genuine mistake that has been corrected isn't the best way to impress a new employer, so accept the change without fuss.