I mean, its a very common pathway and the reason that many people are more than happy to take public sector jobs that aren't super well paid. Being influential in the public sector simply means that you can jump ship to a very very well paid role in the private sector.
Its hard to avoid but when people are advising people on how to bend/break the rules in the very industry they should be acting against in their current role, thats bent. The question then becomes "how can you trust that these people aren't effectively working for the companies they should be fighting whilst they are still in their government role". Paving the way for their lucrative move into the public sector.
Unfortunately you can be pretty sure that all these powerful ex politicians are selling the country and influence/secrets to the highest bidder once out of office. Blair was estimated to be worth about £60m....in 2014. His salary as PM was about £180k/year in his final year as PM which was 2007.
You don't accumulate that sort of wealth that quickly without being of massive massive value to very wealthy people and knowing the right poles to grease. They're largely all as bent as a nine bob note.