Initial disclosure: I work as a photographer and licensing my images is how I earn my living, so my perspective will differ in some ways from other contributors here.
With that said, because you are dealing with UK law, there a few facts and precedents which are relevant regardless of opinion; firstly, you should have a read over this primer on how copyright works with respect to photographs in the UK
https://www.gov.uk/government/uploads/system/uploads/attachment_data/file/481194/c-notice-201401.pdfSecondly, you need to know there are no time limits as to when court actions could be taken regarding copyright infringements in the UK; this was established in case law back in 2009
http://www.bailii.org/uk/cases/UKHL/2009/41.htmlThirdly, whether your wife profited from using the photograph is generally not taken into consideration in the courts, nor would consideration usually be lent to your claim that her website is not a money-making enterprise; case law exists that establishes a correct measure of damages during proceedings is ordinarily the lost revenues of the claimant.
http://www.bailii.org/ew/cases/EWPCC/2013/26.htmlI should state that a claimant does have leave to request an accounting of profits if there was evidence that unlicensed use of a copyright work was for commercial gain e.g. as part of an advertisment, or a product that is sold either publicly or privately.
Damages assessments can also allow for uplifts for willfulness and other factors
http://www.epuk.org/news/aerial-photographer-s-damages-claim-achieves-record-heightSo, a claimant offering settlement for the sum of £850 if settled promptly might, at first blush, appear to be unreasonable, but there are factors to be weighed as to whether this is really the case.
The size (pixels) of the image as used by your wife, as well as the nature of use (commercial, editorial or advertising) and duration will all factor into what fee stockfood.co.uk would have otherwise offered the photograph in question to your wife. That sets the starting point.
If they can argue / prove that your wife in any way has knowledge of copyright law, or reasonably should have known about it (via her education or employment), then the door is open for willfulness uplifts.
You should use stockfood.co.uk's own license calculators to find out what it would have cost your wife to legitimately license the photograph in question from them - it looks like they offer licenses starting from £19 for editorial uses, and up several hundred pounds for other types.
You should also check that the photograph in question isn't offered for legitimate license by any other outlet; if it is offered by another outlet, then the basis for their claim becomes less clear... but do be aware that many companies syndicate their photographs to other agencies and will, in return, receive a cut of any licensing revenues from such partnerships - so finding it for sale on a different website does not automatically mean that stockphoto.co.uk have no grounds to send their letter to you.
You are always within your rights to ignore any settlement offer that is put in front of you, and you are also free to make a counter-offer if you feel that doing so would be in your own best interests.
My
opinion would be that, if you can prove that your wife
could have licensed the photograph from stockfood.co.uk for quite a bit less than their £850 offer, it may be worth your while offering whatever sum that is so as to settle the matter.