Are there abused or disenfranchised groups you do support payments being made to as a form of compensation? Paying out clearly does nothing for Turing, I mean that payment to those still alive could be helpful. For example, the New Zealand government has paid out groups that suffered due to government action like land unfairly taken. I fully support this.
The NZ government continues to make payments to Maori (an indigenous people lostlogin refers to). Maori are in a socioeconomically inferior position overall, partly (largely?) as a consequence of European misdeeds less than two centuries ago. I think most people who know of the similar (but much worse) socioeconomic positions of the Australian Aborigines and native American people will probably agree making compensation is the right thing to do.
Suppose however that the Maori had a socioeconomically superior position. Would it still be the right thing to do to pay them for past misdeeds? Technically, I would say yes. Practically, probably not.
As an illustrative example, consider the way Chinese immigrants were treated during the gold rushes ~1850-1900. Though the situation is somewhat different; I'd contend that if Maori were being compensated only for past misdeeds, descendants of Chinese immigrants from that time should be also. (But of course Chinese people are in a higher socioeconomic group than Maori).
[Warning: speculation rife in the following paragraph]
So, the NZ government pays Maori because it's a politically acceptable (politically beneficial, probably) way to provide Maori with some stimulus to increase their socioeconomic standing. I expect that had Maori been able to summon the socioeconomic standing (and corresponding political power) earlier they would've received compensation earlier. Had they never had a relatively lower socioeconomic standing they may never have felt aggrieved as a result of wrong-doings and not pursued payment at all.
An aside: Another complicating factor in the NZ situation is that the legal basis of Crown ownership of NZ is somewhat shaky. There appears to have been some "mistranslation" that occurred in the Treaty of Waitangi, meaning Maori believe they are the sovereign owners of NZ, while The Crown believes it is.
Sorry, I don't, because where does it end? IMHO, it's nothing more than a token gesture. Financial compensation won't change the wrong that has been done. It's superficial and ever so slightly patronising. It's symptomatic of the vile litigious happy culture that we find ourselves in.
A recent example of where the UK was, in my opinion, quite right in paying out to victims was to people who had been tortured by British colonial forces during the Mau Mau revolt in the 1950s:
I would also support compensation for anyone who was a victim of extraordinary rendition through the UK and criminal prosecution of anyone who aided this ghastly practice.