Don't have any direct experience in foreign private equity, probably because it's not that common among individuals.  In the US, individuals would generally have to be accredited investors to participate.

Here's the way I'd look at this.  First of all, my understanding is that private equity firms in the UK are generally organized as limited partnerships, which are PTE's, just like in the US.  Assuming all partners have limited liabilities, the default classification would be an association for US tax purposes.  It would be eligible for CTB election to be treated as a partnership but I doubt the UK limited partnership would have made the election.

If the UK limited partnership is an association (i.e. a corporation) for US tax purposes, we'd then look at whether it is a CFC and whether your client is a 10% US shareholder.  If not, we'd look at whether it meets the thresholds under either the gross income or assets test to be treated as a PFIC.

It may not be that simple to determine whether the UK limited partnership is a PFIC because some private equities may actively run the assets they acquire for turnaround over a number of years while others may hold smaller stakes as long-term investments.

My take is that you have a lot of work cut out for you and you may not be able to obtain all the pertinent information from the private equity firm through your client because much of the information may be privileged and will not readily available by virtue of this being a private equity firm after all.

Depending on the size of your client's investment and scraps of information you can gather (including agreements and prospectus your client should be able to produce), you may need to make a call to the best of your ability and build a defensive position.  International information returns are a landmine for the unwary.  Not only could there be substantial monetary P&I, failure to file these information returns with complete and accurate information would also toll the SoL, as you probably already know.