The last Labour government enacted significant measures to make sure trusts were much less attractive for tax planning in the UK. The latest evidence on the number of trusts declaring income for tax purposes (which may not of course indicate all trusts) suggests that this had a significant impact upon their use:
The data indicates significantly fewer trusts in use earning significantly less income.
Which does not mean we do not need a public register of trusts by the way: I firmly believe that we do.
But it's good to see that measures to beat tax avoidance do work.