As the FT-SE 100 index put on 9.7 points to 3,532.4, shares of the telephone giant were pulled from their year's peak by blunt sell advice from the investment house.
At the start of trading, BT shares pushed ahead. Then details of the Fleming's caution circulated and the price ended 2.5p down at 410.5p.
The securities house believes they should be around 340p. It says the market has failed to appreciate just how difficult it will be for BT to top pounds 3bn profits this century.
A range of influences, from regulatory and competition pressures to the cost of international expansion, will, it is argued, depress profits, which Fleming estimates will reach pounds 2.85bn this year; pounds 2.92bn next, and then slip to pounds 2.88bn.
But Securicor, minority shareholder in BT's Cellnet mobile telephone operation, managed to dial into the market mood with the ordinary shares up 30p to 1,760p and the non-voters' 25p at 1,228p.
It is generally accepted that BT is anxious to buy full control of Cellnet and there have been indications the telephone giant has successfully pressed its case in Whitehall. All that remains is for BT and Securicor to agree a price.
With New York managing a firm opening, more mortgage rate cuts and UBS lifting its year-end Footsie forecast to 3,600, shares were in the mood to move to new high ground, but in thin trading a little late profit-taking took its toll.
BSkyB, the television group, rose 4p to 351p as Barclays de Zoete Wedd and Goldman Sachs prepared to sell all, or most, of Pearson's 9.75 per cent shareholding. Pearson, helped by a well-received presentation, gained 10p to 630p.
Some operators are talking about cashing in their BSkyB shareholdings and switching into Nynex, the cable TV company that floated at 137p in May and is now 119.5p. The shares are expected to be recruited into the FT-SE 250 index, which could provide the spur for a re-rating.
Vosper Thornycroft, the shipbuilder, was at one time 66p higher at 968p as talk of a British Aerospace swoop went the rounds.
The shares ended 31p up at 933p. An institutional visit to one of the company's sites could, however, have provoked the latest interest.
Yet Vosper is regarded as being in play, with BAe likely to pounce following its failure to capture VSEL. BAe climbed 10p to 660p.
Taunton Cider jumped 29.5p to 212.5p as suspected takeover interest was confirmed. Matthew Clark, the owner of the Gaymers cider business, is regarded as the most likely predator. Its shares fell 9p to 659p. But HP Bulmer, up 5p to 493p, could also be in contention. United Biscuits was disconcerted by the poor Hillsdown Holding figures and uncomplimentary advice from ABN Amro Hoare Govett and BZW. Grand Metropolitan added 8p to 424p on talk of corporate action and positive NatWest comments.
NatWest was responsible for driving insurance shares higher, with Sun Alliance up 8p at 345p. Properties weakened on UBS uncertainty. Builders improved a little on the round of mortgage cuts.
Utilities remained firm on takeover hopes. The generators were particularly strong with National Power up 9p at 530p and PowerGen 9p at 590p.
RTZ, interim figures today, rose 17p to 880p. Societe Generale Strauss Turnbull has a 1,000p target price. Rexam, the packaging group, edged ahead 2p to 423p with a presentation due today; Racal Electronics gained 5p to 282p on Smith New Court support.
ML Laboratories, firm on Monday, rose another 17p to 226p on encouraging tests for its anti-Aids treatment. Celsis International, the health group, rose 13p to 112p as Yamaichi, the Japanese securities house, said buy, suggesting a year-end price of 180p. Scholl, the health care group, romped ahead 45p to 239p as it reported a strong profit advance and hit back at a shareholder rebellion led by South African agitators Julian Treger and Brian Myerson.
Unipalm, the computer group, crashed 37p to 418p on worries bid talks had become bogged down. But the company said they were on schedule. Telspec, an electronics group, jumped 24p to 606p following interim results. The shares were floated at 160p in December, 1993.
A profit warning and departure of the chief executive reversed Central Motor Auctions 10p to 58p and Alliance Resources shaded a further 0.25p to 4.25p on US worries. Antonov's remarkable ride continued, up 8p at 146p.
Hobsons, the food producer, was busily traded, ending unchanged at 29p and Budgens held at 36p after a 2 million agency-cross at 37p.
o Brown & Jackson, the troubled Poundstretcher retailer, continues its long, painful recovery. Its rights issue attracted an 87.2 per cent take-up with the support of Pepkor, the South African heavyweight, crucial. The South Africans now have nearly 65 per cent of B&J, which lost pounds 9m in its first half-year. Once B&J is turned round Pepkor could be tempted to merge it with its Your More Store chain, operating mostly in Scotland. B&J shares fell 4p to 33p; they have been 54p this year.
o Wilson Connolly, the builder, rose 4p to 163p with Williams de Broe forecasting profits, due on Friday, emerging at pounds 40m, up from pounds 38.2m. Although it expects the company to accompany its figures with a cautious trading statement it regards the shares as a buy, encouraged by long-term prospects.