Nationwide Building Society recorded a 0% month-on-month average in March after a 0.4% rise February.
It said the annual rate of price growth was stable in March at 3.9%, which was unchanged from February. The average UK house price in March was £271,316.
Robert Gardner, Nationwide's chief economist, said: "These trends are unsurprising, given the end of the stamp duty holiday at the end of March."
Uncertainties
He added: "The market is likely to remain a little soft in the coming months since activity will have been brought forward to avoid the additional tax obligations a pattern typically observed in the wake of the end of stamp duty holiday...