The transaction is subject to the satisfactory appointment of a contractor and other conditions.
It will become unconditional and fully secured once the conditions have been met, which is expected in the next few months.
Planning permission for the scheme was granted in late 2019, subject to a Section 106 agreement.
Construction is expected to begin in H2 2020, with Blocwork — a 50:50 joint venture between Network Rail and Bloc Group — the developer of the scheme.
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Grainger expects the investment to generate a gross yield on cost of over 7% once stabilised, which is estimated to happen by early 2024.
Helen Gordon, chief executive at Grainger, said: “Our rental housing scheme on the Queens Road will represent great value for renters with long-term, flexible tenancies, professional on-site resident services team, high speed broadband, and communal spaces and amenities such as a lounge and gym.
“We look forward to bringing this scheme forward swiftly with Blocwork Group.”