I fly a number of non-transponder equiped aircraft and regularly get clearances through the East Midlands CTA without any difficulties. Sometimes they ask for a 30 degree turn to get positive radar identification, but usually they accept my position report which corresponds with their primary return.
Like Mike Cross, I too would like to buy a transponder but had to postpone my purchase when the mode S fiasco started. Yet another example of legislation reducing rather than enhancing safety.
I believe that using correct and accurate RT makes a big difference, and I cringe when I hear some of the requests made to Radar Controllers.