As an aside on the 6th of August I was inbound to LCY and as the aircraft turned onto base I observed a light aircraft pass under the Dornier offset approx 250" and below by slightly more, couldn't comment on the slant range but it was quite alarming
It's very difficult to judge the vertical separation of other aircraft. You may well find that your 250 ft was actually 500 ft and no one entered CAS without clearance. It is very common for aircraft to fly right up to the 2500 ft base.