In an earlier contribution to this discussion,
Phil wrote:

The 1/2 brick wall may not be strong enough to carry the RSJ and it's
imposed loads - you will need a structural engineer to show this and
provide a solution.

If it's only holding up a floor - and not any other brickwork and/or
supporting the roof - it will probably be ok. After all, the other end of
the RSJ will probably only be supported by the inner leaf of the cavity
wall, which is - in effect - a single brick wall. You don't get much support
from a cavity!
--
Cheers,
Set Square
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