However if we pay cash because of an explicit offer to reduce the cost of the work, and because this reduction is due to the evasion of income tax or VAT, then we are formally co-operating in evil, and committing a sin (probably a venial sin given the amount of tax normally involved.)
If you want to get out your catechism and play lawyer, you'll find the tax has to come from a legitimate authority. Father Finigan is in the U.K., and their Consitution is unwritten, so it is probably less easily for them to point out the government is in flagrant violation of it. However, obviously the anarchist and libertarian arguments apply. The monarchists could also marshal a few arguments too.
But formal cooperation with evil, all one its own, ought to be enough.
If you pay the tax, when you can avoid it, you are formally cooperating with abortions, wars, quite possibly a bit of euthanasia here and there, entire populations of children being miseducated and propagandized into direct opposition against many doctrines, etc...
Additionally, the much vaunted principle of subsidiarity, for it to actually work, would suggest a transaction between two people ought to stay between those two people, unless they decide they need some arbitration or some other kind of help. We've been trained to presume the government simply has the right to intrude, yet it was not so when most of these doctrines were created. Nor were governments occasions of formal cooperation with as many mortal sins back then.
Father Finigan seems to be a pretty good priest. He's been attacked by the press in his country, so he shut down his comments, and this little post is in no small part, a substitute for a comment. I am not going to lay out the point by point here, because you can do that if you want, as I suggested above.
The thing is, you have to want to. You have to understand that you can't serve Christ or your fellow man if you tie your hands in this way. These taxes have a direct destructive effect on our local communities and they are part of the reason our societies don't work anymore. The first thing we need is protection, then we need to figure out how to rebuild.