"Benefits fraud costs the government £1.3bn a year, according to official statistics, while the gap between tax owed and tax paid is put at £34bn a year by officials."
https://www.theguardian.com/uk-news/2016/apr/13/benefit-or-t...
I actually still get a bit more upset over benefit fraud than tax fraud, as (disclaimer) my family are beneficiaries due to my brothers autism - the hours and stress required to successfully navigate the system cannot be underestimated. Most recipients of disability payments etc will tell you it is a full-time job. The moral failure of benefit fraud is paid for twice - once materially by the taxpayer, again spiritually by the recipient. For me, another argument for the qualitative moral and social components of education - which seems to have been stripped away of late... A rant for another time!
Basic income for everyone would be one way, but that brings its own set of issues and challenges with it
I agree we need to concentrate more on tax avoidance. Particularly since any welfare state is going to be abused by a minority of some people - that is not a good reason to create a totally ineffective welfare state - that is part of the price we pay for it unfortunately.