@Sunflowergirl1
I think they try but it is so utterly vast and now the norm that it is impossible.
No, I don't think they even try anymore. As an accountant, I'm legally required to make "suspicious activity reports" for illegal activities, such as tax evasion, and in the 20+ years that regime has been in place, I've made a few dozen such reports, usually highly detailed with reasons, evidence, etc., so basically VERY easy for HMRC to investigate. Out of those few dozen reports, not a single one has led to any kind of enquiry/investigation that I know of. It's just a statistic gathering exercise. On courses I've been to, lots of other accountants have said the same. Very difficult to find any who've had any kind of response/action from such a report. And let's not forget, these are the EASY cases where lots of detail has been given to HMRC, but they still choose not to take action.
Brown really screwed things up with all his reorganisations and amalgamations of the tax offices etc., added in to giving HMRC responsibility of state benefits such as his stupid tax credits, which soaked up massive amounts of HMRC manpower, not to mention lots of fiddling around making the tax system even more complex. Huge numbers of experienced tax inspectors were made redundant and replaced with poorly trained call centre workers.
But, as you say, tax evasion, benefit fraud, illegal working and the black economy in general is now so utterly vast, it's hard to see how anyone can turn it around, but it's still getting worse, so someone should at least try.
What's more annoying is that you get an automatic £100 fine if you are a day late with your tax return, which HMRC DO pursue you for, but if you're a "too difficult" case, like a rogue tradesmen doing VAT free cash in hand work, they are too lazy to bother investigating and challenging! Those engaged in tax evasion know that they are basically free to get away with it as long as they put "something" in their tax return and submit it on time.