The appeal to the Treasury for more funds follows a disclosure that the Government has shelved its pounds 2bn plans to step up basic security in prisons.
A massive security package proposed after the break-out from Parkhurst top security jail last year now seems certain to be put on ice.
The pounds 2bn price tag is the estimated cost of implementing 73 of the 127 recommendations laid down by General Sir John Learmont in a review of prison security.
Most of the money was to bring jails up to minimum security levels, but Home Office officials say this is too costly and suggest stalling the plans.
In a draft report to the Home Secretary, they say a timetable could be published mentioning only those recommendations which do not require funding.
"Ministers could state that the omitted recommendations were those which were still undergoing study," said the draft.
"The other alternative," it continued, "would be not to publish a timetable. If Parliamentary Questions were raised, this omission would have to be justified. It could be attributed to the complexity of the recommendations demanding a more protracted study and evaluation."
But Mr Tilt, the director general of the Prison Service, warned that the growth in numbers of inmates was "extremely worrying", and said that new accommodation for inmates must be built. He pointed out that the number of prisoners in British jails has risen by 4,000 in the past 12 months.
Part of the increase is believed to be a result of the Crown Courts responding to calls from the Home Secretary, Michael Howard, for more custodial sentences and longer jail terms.