The U-turn means that the key recommendation of General Sir John Learmont's inquiry into prison security has been abandoned. After the attempted breakout of IRA prisoners from Whitemoor jail and the successful escape of three dangerous inmates from Parkhurst last year, the General said in the autumn that Britain needed two "supermax" jails.
One of these, he said, would be for terrorists and major criminals; the other would be for psychotic and disturbed inmates who could not be controlled in ordinary prisons.
But an internal Prison Service feasibility study, chaired by Robin Halliwell, a former governor of Strangeways, has decided that it will not be possible to open either of the prisons, civil service sources said.
Treasury spending restrictions have forced the Home Office to consider allowing private security companies to build and manage the two jails - at a cost of between pounds 60m and pounds 70m each.
A leaked memo from the feasibility team has already warned that this course of action may "attract negative tabloid interest ('Group 4 to run British Alcatraz', etc)".
The civil servants have found it impossible to see a way round the Treasury rules and get the experienced public sector governors and officers the prisons will need if escapes and riots are to be prevented.
They have also concluded that the political fall-out from any escape from the most secure prisons in Britain would be, as one mandarin put it, "too embarrassing to manage".
Officially, no decision will be made until February next year. But ministers have privately told civil servants to put a British Alcatraz on the back burner and the feasibility study group has been winding down.
The group will recommend that any available money should be spent on keeping dangerous prisoners secure in four or five existing jails around the country.
Jack Straw, shadow Home Secretary, said last night that the reports showed there was now an intense squeeze on the Prison Service and that Michael Howard, the Home Secretary, had taken "a bloody battering in the public expenditure round".
Spending will fall by 5 per cent in the next financial year and continue falling until 1998.
Meanwhile, the number of prisoners in British jails is growing rapidly. Mr Howard's "prison works" policy has seen it rise from 40,000 in early 1993 to 52,000 this year.
If Mr Howard implements the tough plans that he announced at this year's Conservative Party conference to impose harsher penalties for burglars and drugs dealers and to reduce remission for existing prisoners, the already bursting prison population will rise by an estimated 20,000.
Harry Fletcher, spokesman for the National Association of Probation Officers, said: "There just isn't the money and space for Michael Howard to be tough. Where's he going to put all these people?"