Customers for 3-series models are being told they will have to wait till November.
Sales of the 3-series, the smallest in the BMW range, have soared by almost 22 per cent this month compared with an overall rise in new car sales of 2.6 per cent.
The surge, helped by the traditional August scramble for newly-registered cars, has caught dealers by surprise and most have run out of stocks. BMW plants in Germany are shut for a 19-day holiday.
Worst affected are the four- cylinder 316 and 318 models (particularly the convertibles), though the dearer 320 and 325 vehicles are also facing tight supply. Prices for the 3-series, the cheapest in the BMW range, start at about pounds 15,000 and are being raised by an average 3 per cent from next month.
A BMW spokesman said: 'If we had produced enough cars, this would have been our best August ever. Demand has grown steadily all this year.'
BMW's strong sales contrast sharply with a generally disappointing start to car sales this month. August accounts for about a quarter of the year's car sales. The company's share of the UK market has risen from 2.8 to 3.32 per cent.
Edward Stanford, motor analyst with Albert E Sharp, said: 'BMW are not producing enough. But it is beneficial for the dealers as they don't have to discount prices.'Reuse content