If permission to proceed is granted by the Court the case will be considered at a full hearing, likely to take place next spring or summer.
Weston Homes and Columbia Threadneedle will claim the housing secretary acted unlawfully in refusing permission largely on heritage grounds.
In 2018, Norwich City Council voted in favour of the proposed scheme and resolved to grant planning permission.
The proposals were then called in and despite the Planning Inspector being in favour of the proposals, Jenrick decided to refuse permission.
The High Court will now review his decision.

The decision could jeopardise the £15m of government Housing Infrastructure Fund money already allocated to accelerate the development of the site.
The Anglia Square redevelopment project would represent a massive investment in Norwich City Centre, providing up to 1,250 new homes, including a 20-storey tower, hotel, cinema, new shops, enhanced public realm and car park.
Bob Weston, chairman of Weston Homes, said: “Having taken legal advice at the highest level Weston Homes and Columbia Threadneedle have decided that we should take High Court action and seek to get Robert Jenrick’s decision overturned.
“At a time of extreme economic hardship and with Norwich on the edge of a deep recession the Secretary of State chose to refuse a massive investment opportunity for the city.
“His decision flies-in-the-face of Government policy on housing delivery and encouraging brownfield-land regeneration in order to protect the greenbelt.”