HMRC work on "honesty" for virtually everything, whether IHT returns, self assessment, VAT returns, etc. The days are long gone where you had local tax inspectors sitting in offices looking through piles of bank statements/invoices. The chances of anyone ever getting any kind of challenge, enquiry or inspection by HMRC are pretty much zilch these days. Of course, there's always a risk of a random inspection (often done by newly appointed inspectors to gain experience), and sometimes there is "intelligence" that triggers an inspection such as something thrown up automatically by the HMRC computer when cross referencing one database against another (such as benefit records, land registry property transfers etc). Sometimes they have a kind of "task force" looking for a specific type of thing with a small team of inspectors specifically interrogate various databases looking for specific transactions etc.
It's akin to traffic offences really. Your chances of being caught driving without a seatbelt or looking at your mobile phone or driving without a valid MOT or going through a traffic light just changed to red, are pretty much zilch. Police driving around aren't generally looking for that kind of thing and probably in a World of their own and wouldn't notice anyway. Yet, sometimes, there'll be a task force set up for those exact offences and there'll be a small team of officers parked up specifically to catch people doing one of those things, so occasionally your "chances" of being caught are higher if you're in the wrong place at the wrong time.
Back to IHT, HMRC already have databases of "big" transactions, i.e. house conveyances, large bank transfers, so it would be pretty easy for them to interrogate those databases for any probate applications that are large or otherwise look a bit strange. They'll also have self assessment tax returns going back years for people who've had to complete and submit them, i.e. higher earners, those with lots of income from interest and dividends (indicating large savings). They also have a database of ISA accounts (banks have to report via National Insurance numbers). Also databases of people's pension contributions (as HMRC administer the tax repayments to pension schemes).
So they have a lot of information that they "could" cross reference. Whether they do or not is a different story. Personally, I see very little signs of action from them which has been the case for 20-30 years hence my initial comments about there being very little risk of being challenged, especially for relatively small/simple estates and even moreso for people who've kept their head below the parapit and not drawn attention to themselves!