If there is a brick wall above then the one below is supporting its weight so you will need a bit of steel in there, you may well end up with a bulkhead at ceiling level to hide the steel unless you can build it into the depth of the floor and get the first floor joists to bear into the web somehow.
RSJ's are not that expensive, £100 should be enough.
The building regs thing only becomes an issue if a potential buyer spots the work and asks to see the approvals.