The warnings come days before the Bank's monetary policy committee is thought likely to increase the cost of borrowing by another quarter-point to 7 per cent. It meets on Wednesday and Thursday.
New calculations by David Walton at Goldman Sachs suggest that the consumer windfalls could have added up to pounds 2bn to spending during the first half of this year. "This suggests there is plenty of scope for retail sales to receive a further substantial boost during the second half of the year," he writes.
Anecdotal evidence suggests that spending on items such as foreign holidays and cars - neither included in the official retail sales figures - has soared since June.
Another expert warned yesterday that interest rates should rise to 8 per cent to avoid an inflationary boom, despite the punitive impact that would have on exporters.
Chris Wright, economics director of Barclays Bank, said: "On balance, the best chance of avoiding a more volatile growth and inflation cycle still seems to be to raise rates further."
So far this year the flotations on the stock market of Alliance & Leicester, Halifax, Woolwich and Norwich Union have given millions of people free shares worth pounds 22bn in total. More than a fifth were sold immediately.
It is impossible to be certain where this pounds 4.5bn has gone. But, comparing retail sales in the first half of this year to the level that would have been expected given rising incomes and falling unemployment, Mr Walton estimates that the extra boost has amounted to pounds 800m.
With retail sales accounting for only 40 per cent of consumer spending, this implies a pounds 2bn boost to the total from the share windfalls so far.
The rest will have been put into other forms of saving. The Building Societies Association reported the biggest monthly inflow of deposits since 1986 during June, and suggested this was caused by carpetbaggers looking for the next society to convert. The inflow amounted to pounds 1.8bn in June compared with pounds 878m in May.
Sales of PEPs and unit trusts also roared ahead, although the main high street banks reported that retail deposits in June rose by slightly less than the recent monthly average of pounds 2.1bn.
A survey conducted for the British Retail Consortium suggested that eventually about a third of the bonanza shares, expected to add up to pounds 35bn by the end of 1997, would be sold.
Mr Walton estimates that if half of this amount were spent, and the rest saved, the direct boost to consumer spending would be pounds 5.5bn.
There could be an additional indirect effect from reductions in other forms of savings as a result of holding the new shares.
According to the BRC survey, people are most likely to spend windfall money on holidays (33 per cent), new kitchens, bathrooms and home improvements (20 per cent), household goods such as carpets and furniture (17 per cent) and cars (11 per cent).
In addition, more than one in eight said that they would use windfall receipts to pay off other debts.
The second quarter of the year brought a sharp increase in the proportion of borrowers up to date with their payments on credit agreements, according to Equifax, the credit scoring agency.