At some point, the rise in the price of houses and other goods and services in the non-tradeable sector of the economy would have begun to spill over into the general price level. Wages and other costs would have started to rise. Other things the same, exporters would have found themselves squeezed by these rising costs.
In other words, they would have been squeezed by a rise in the inflation-adjusted exchange rate. So no matter what policy the Bank had pursued, the real exchange rate would have appreciated considerably, and exporters would have been put under pressure.