Good news is that there is a very cheap resoution after all! And far less technically challenging.   Rather than ~£1.5k on flitch beams, Nicks idea of reinforcing the joists beneath the partitioning wall is a green light.   It requires some specialist material rather than plywood, but a 45mm thick Kerto S beam affixed with ESCR screws to each joists will reinforce them enough according to our engineer. Only about £200 after delivery fees. 
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