When claiming payment from an infringer it's advisable to think through the possible outcomes when considering how much to charge. The infringer has forfeit the right to negotiate price by using without permission, so within reason you can charge what you like. However you want them to settle early and easily, to avoid the expense, complication, delay and uncertainty of court action. Therefore how much you charge ultimately has to be defensible in court, but reduced sufficiently to encourage them to settle.

If you were to sue in a UK court, the damages for infringement would be based upon the market value of the use that the infringer has made of your work, increased perhaps by an amount that the court deems appropriate for flagrancy of the abuse. UK courts are restrained about this, unlike the US where punitive multipliers of up to 70x are applied for infringements against registered works. UK damages are closer to the US case for unregistered works, which are limited to 2x the lost revenue.

What this means is that the more flagrant the infringement and the better your evidence the more you can charge, but probably it should be no more than 2 or 3x the going rate.

If you win the case you would normally also win your costs from the infringer. So these costs can also be factored into your proposed settlement figure.

Because market value is central to damages, you will have to convince the court that the value you place upon your work is realistic. The other side will almost certainly try to challenge your valuation. For that reason you have to stay close to 'the going rate' unless you can prove that the work had exceptional value, either because you are able to command exceptional rates or the work itself is rare or exclusive or has required unusual skill and effort. If you are able to produce proof of previous sales at higher rates, so much the better.

So you need to base what you charge on the going rate, adjusted for any special considerations. Useful resources for finding out rates are the price calculators at Alamy and Getty photolibraries (you will need to register with these), and the NUJ Freelance Fees Guide (accessible to anyone).

NB: if you have a lot of work placed with microstock libraries charging (say) $1 per Royalty Free image, you have shot yourself in the foot here. Since you have established your going rate is $1, infringements are simply not worth pursuing.

Your final price will therefore be a calculation based on all of the above. This may of course be sufficiently high that the infringer will likely baulk at your offer of a retrospective license. A proven tactical device is to offer a sizeable discount for early settlement, say 30% off for settlement within 7 days.