Cost? - nearest I've come to something like this was close to 7 figures.
We're basically talking hundreds of thousands rather than tens of thousands imho. Best guess would be 150k upwards as a start point given the brief.
The enquiry starts now and is due to conclude in November.
Day rates for good investigative analysts start at around £500 per day. They can go much higher. There will be more than one person - possibly up to 10 not necessarily all working concurrently though - depends on what specialisms are required re: the specifics of the remit and it's relative importance.
A lot depends on if they've done a fixed price deal for the job or T&M. In the case of the latter you're not just paying for the consultants but their expenses too - travel/accommodation etc
All that said I'm basing this on a business, rather than political "consultancy shakedown" situation.