I would agree with Mathews point on wiggle room. Bringing an action in the High Court is a lot of work for the claimant and thus I am sure most if not all claimants , would prefer an out of court settlement , even at a significant discount. They will naturally claim at the higher end of what they consider reasonable.
How much they can claim depends on various factors including the normal selling price of the work in question, the extent of the use and the behaviour of the parties, both in relation to the infringement and their behaviour during litigation.
My own personal view, and unfortunately I have no evidence to back it, is that there are two types of claimants, those who intend to pursue the claim and those who are bluffing and have no intention of ever bringing a claim.
If a claimant were the latter type then I can see that it they may be tempted to issue a vastly exaggerated claim because it is never going to be censured by the courts.
When considering whether a claim is exaggerated, one cannot just look at any given figure of X GBP and say whether or not it is exaggerated. It all relates to the value that that particular work is normally sold for plus any aggravating factors. Most Copyright Infringement Claims involve photographs and the value of a photographs in general can vary wildly from free, to a few pounds to thousands of pounds for a single image.
Now the normal licencing costs may be a starting point but there are other factors to be considered as well, eg has the defendant also altered the image, removed a copyright notice, meta data etc etc. In the UK the IPEC has awarded 20x the normal Value of a work ( Absolute Lofts South West London Ltd vs Artisan Home Improvements Ltd & Darren Mark Ludbrook [2015] EWHC 2608 (IPEC) ) Thus I personally , would consider a claim exaggerated if it was in excess of 20 x the normal value of the work, unless there were exceptional circumstances. ( eg the defendant made a lot of money from the infringement )
The figure mentioned of 10 x the normal value of the work is not necessarily exaggerated, however to achieve it court, the claimant would have an awful lot of work to do and would have to show that the defendant was particularly outrageous or made a lot of money from the infringement. If it were to go to court, I think if the case was a fairly standard infringement and not particularly outrageous then the court would likely award a lower amount. I would not see it as exaggerated per se but merely the starting point for negotiations. This is just the way litigation works. As defendant your starting point would be the normal licencing cost of the work. Having a starting point of Zero is not helpful in reaching a settlement and would almost certainly have a negative influence on damages if the case does go to court. Whatever the starting point and whether you are a claimant or a defendant, you should expect to move your position nearer your opponent during negotiations.
In all the case judgements I have read, and I have read an awful lot of them, no defendant has ever been found liable for copyright infringement and then been awarded zero damages, indeed the EU Directive 2004/48/EC on the enforcement of intellectual property rights, states that the courts must award "at least the amount of royalties or fees which would have been due if the infringer had requested authorisation to use the intellectual property right in question". The Directive is online and is essential reading for anyone involved in IP litigation within the EU. It also takes precedence over UK statute law -
http://eur-lex.europa.eu/legal-content/EN/TXT/HTML/?uri=CELEX:32004L0048R(01)&from=EN Article 3 of the above states that damages must be "dissuasive" which indicates that they should be rather more than the normal value of the work. Copyright Infringement would not be dissuaded if copyright holders were forced to undertake time consuming litigation, only to be awarded what they should have been paid without litigation. Thus almost all of the IPEC SCT cases I am familiar with have resulted in damages significantly more than the normal licencing value of the work, typically in routine cases 2x to 6x.
One point I should mention, is referring to defendants in general as victims is unhelpful. As with a large proportion of Civil Litigation, both sides may regard themselves as Victims. From a legal point of view the Victim will be the one who has suffered loss due to the unlawful conduct of the other party. Where one is a defendant in a case where ones own conduct has been unlawful, a more apologetic and reasonable negotiating stance is likely to achieve a better settlement outcome , or , should reasonable negotiations fail, would be looked on more favourably by the court.