Money is thus going from the taxpayers out of the country, with no benefit to the U.K.
But there is a benefit to the U.K as it's generating a return for pension funds. Where do you think pension assets are invested? In providers such as Aviva, L&G and BlackRock which invest those assets to make a return for U.K. pensioners (and indeed investors in ISAs etc). It's also providing a source of funding for U.K. developers.
If you want to extend the argument, what about tax relief provided on pensions invested in US assets? The S&P 500 has delivered some stellar returns in the last two years if any UK investors have put that in their pensions but it's also outside the UK (and domestic ownership of U.K. shares is at a historic low).
Chasing out institutional pension funds or private landlords will have the reverse effect on rental prices. Building more social housing and reviewing eligibility for council homes would be more effective.