I'm pretty sure they will find more than that. If they look in the right place.
Why pay someone else when they fail to harvest data they already have?
Tax credits were handed out like cornflakes, there is no validation. I would imagine if they cross checked between tax returns / PAYE a good portion of the £23.7B would be up for grabs.
Housing benefit looks the same. £400 per week for house £280 week for a flat rental. Not sure how many people who don't work need to live anywhere that expensive? I wonder how many have had pay rises / changes in circumstances that would mean they are no longer eligible?
Also they should make the decision that if they are long term unemployed they leave the city centre unless they are willing to fund it themselves.
So there is £45 Billion in two benefits that could be tracked by correlating information already held by HMRC. (2009 figures)
Child benefit could be administered via PAYE / tax return which would reduce costs, allow gentle tapering and those who weren't working could be dealt with via Tax credits etc.
Now when they have done all that they can start with other government databases, DVLA, car insurance ( I would imagine named drivers could be interesting) , Land registry (I wonder how many people claiming benefits have properties), tenancy deposits (likely to be in joint names), bank transfers / holdings over £10k.
Of course they could also get details of anyone charged with a crime and investigate those as well so they can assist the police with proceeds of crime. They may also find they have other sources of income they haven't declared such as burglary.
When they have done all that they could try Experian.
But no lets harvest private data, wonder how soon my credit rating will end up in Nigeria?
A cynic would suggest that someone is looking for a directorship.