Probably because you've trained for an engine failure, but not for a radio failure.
I've had several radio failures, and so far failed to annoy anybody with my behaviour, so I'll offer some thoughts.
If you have a comms failure, above all else, fly really really predictably. So, for example, if you are on a planned route and expected at a particular airfield at a particular time - follow that route, join by a method that is obvious and gives everybody a chance to see you (so absolutely no straight in approaches - deadside, downwind or overhead, depending upon local rules: overhead would always be my preference, given a choice - overhead as it gives the airfield more time to see me, and me a chance to see the signal square).
Don't forget that if you have a transponder, and you have time (and still have power!), squawk 7600. If it's working, that means there's a fighting chance of light or flare signals being used for you at your destination.
In any variation on the above case, then go straight to ATC and explain yourself ! That way, the potential for any genuine upset should be minimal.
With regard to inability to get a word in in the circuit, it will depend upon the airport. If it is a controlled airport such that you should normally require a clearance to land, then fly a normal circuit, but go-around early, fly another circuit and hopefully you'll actually manage to talk to them next time. That said, a good controller will know where you are, recognise the problem, and give you clearance and/or instruction when you are on final, even if you didn't ask for it.
If a clearance to land is not required, which is the case at "information" or "radio" airfields such as Popham or White Waltham, then you are well within your rights (subject to normal airmanship) to simply carry on and land, or even do a touch and go.
G