By the time they are over the said large pointy building - I have it on pretty good authority - they are around 3000ft and report that to ATC. So there's the first problem with the report - if this aircraft was at 5000 or 4900 - it would be 2/3rds higher than normal.
Aircraft over that part of London are considerably higher than 3000 feet these days. With Continuous Descent Approaches and being over 13 nm from touchdown they are at least 4000 feet (if not more).