In response to Circuit Bashers's suggestion, I don't think this is legal - I'm pretty sure that the radio insatllation needs to be certficated as part of the aircraft. I'm sure someone else will know more definitely.
I think non-radio flying varies depending on where you fly from (or to). If you fly from a non-radio farm-strip then obviously it won't make a whole load of difference. If you fly from an ATC field, then there's a good chance they won't be happy about you flying non-radio.
The field I know best is White Waltham. There are plenty of non-radio aircraft based there, and on the whole they integrate well with other traffic. That's because all of the based pilots know that they're there, so we always have our eyes open in the circuit, regardless of whether we've spotted everyone who's called "downwind" within the last 5 minutes.
I've only flown non-radio a couple of times, and it was a bit disconcerting, just because I wasn't used to it, but not really a problem. Before leaving, find out as late as possible what the runway in use is - once you've found it out, if it changes you'll have no way of knowing! That's less of a problem in the air, because you'll be looking at the signal square, but signal squares have been known to be wrong!
Like I said, this is only from very limited experience, but I don't think you'll have any problems, depending where your aircraft is going to be based.
FFF
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