I had the same issue fitting the Mike'sXS Brit style mufflers to my 83 Heritage Special. I did what PamcoPete did, and used a muffler reducer to fit up the new pipes to the old headpipes. I used an 1 5/8" ID to 1 1/2" OD adapter to fit them up (you MUST NOT get the OD and ID mixed up. I ended up going back to the store a couple of times..). Here's the issue...the old head pipes did not quite slide into the wide end of the adapter, while the narrow end fit perfectly inside the new mufflers. What I did was swage open the 1 5/8" end with a large 1/2" drive socket. I put the adapter and the socket in line in a vise and clamped them together, forcing the socket into the adapter, thereby swaging it out to the proper dimension. A little oil is recommended to help it all along, although it went very smoothly. The gradual bend between the two diameters was transformed into more of a sharp step, but this was not a problem. The finished product was not quite square, bit it went together without drama. The adapter slipped on over the headpipe end like it was made for it. Once bolted in place, the whole affair was straight and looked factory. Unfortunately, the join was ugly, as the adapter is built for function and not form, since it is hidden up under a car and expected to rust out and fail in normal operation. I then did Pete's trick of dressing it up with a chrome sink drain pipe. Luckily, I know a plumber who was happy to sacrifice a length of drain pipe. He used a pipe cutter to make two equal lengths of 1 1/2" drain pipe just long enough to cover the exposed length of adapter which slipped over the end of the headpipes. I placed these short pipe lengths in a vise and carefully cut them along their length on one side, so I could spread the edges apart and slip them over the adapter. It was actually quite a tight fit. I was worried that the amount of gap I had to open up would permanently deform the covers, but once I got them over the major diameter of the adapter, they snapped tightly into place and looked absolutely factory made! Repeated runs have not adversely affected the fit. They have not come loose, nor discoloured. I was extremely happy with the results. The only issue with these Brit-style pipes is the contact between the center stand stem and the pipe. I cut mine off, but it is pretty hard to use the center stand now, so anyone using these particular pipes may want to put in a bit more effort into solving that issue.
By the way, the old pipes I took off were clamped to the outside pipes only. There were no ill effects from this arrangement. I had suspected that these old mufflers were not the originals since they had removable baffles, and now I see from another post that they are in fact Emgo Widemouth mufflers. They actually have a nice deep bark with the baffles removed.