Is it possible - probably yes. Is it probable - don't think so. Here are a few reasons why:
1) Speed: chasing any landing jet 'down the ILS' isn't really an option for any (bar a handful) of small a/c. And, eve if you could, the relatiive impact speed would be very low (remember, both a/c are moving in the same direction).
2) Wake: I've had my ecounters with wake turbulence and have no desire whatsoever to get into the wake of a 'slow and dirty 747'. Should our Mr. Mad chose to do so, he'll probabaly kiss the ground rather than the bird he's chasing
3) Aim: you've simply got no speed advantage over the jet, hence you'd have to hit on first try. No manouevring or corrections possible. Highly unlikely.
As for the 'circuits in Denham and flying straight into the departure path' bit - if anyone can outclimb a jet in a Cessna or a Piper, please show me how - I'd love to be able to do it ;-) !!