City planners are set to rule in favour of granting Conservation Area and Listed Planning Consent to demolish the general market building and erect a seven-storey development in its place at its planning committee next week.
An EH spokesman said: 'There is absolutely no way we can meet their time scales for a planning committee, especially when you take into account the amount of work that will be needed to go through these plans. We are very disappointed.'
The authority's recommendation for approval has been given ahead of a public inquiry in June that will decide the fate of the iconic market buildings - designed by Tower Bridge architect Horace Jones - which heritage groups say are being destroyed needlessly.
The planners' decision also goes against the Development Plan set out in the Town and Country Planning Directions 1999.
KPF, commissioned by developer Thornfield Properties, has already scaled back its designs from its original nine-storey scheme in a bid to appease heritage groups opposing the scheme, but to little effect.
Adam Wilkinson, of SAVE Britain's Heritage, said the current proposals would be detrimental to the surrounding area, but also agreed that the timings are unachievable.
Wilkinson said: 'We are moving to postpone the public inquiry if we are going to have a fair chance of objecting to the proposals. There isn't a chance we can go through these planning papers with a fine-toothed comb in time.
He added: 'The treatment of the listed Red House is the clumsiest, 1980s-style retention of a facade I have seen for some time.'