Issue one is the Aga CU. That has a normal main switch (not RCD) and an MCB. So a live-earth fault would not trip the MCB as less that 2 amps of fault current would flow. It would stay on waiting for someone to touch it and that someone would become the path to earth.
Does the test button on the RCD itself work?
If not, then this all becomes even more serious as things won't turn off under fault conditions.
Which make/model MFT is it? It could be a faulty RCD, faulty tester, or the tester being blinded by DC earth leakage.