Sure, they could be permanent immigrants, (or undocumented aliens!) I was generalizing the on the idea that travel was not at all impossible, either then, or hundreds of years earlier. The Romans moved large quantities of troops back and forth, and the community of Bath was definitely a Roman tourist venue.
I believe the city of Cirencester was known as corinthium during Roman times. Its at the center of the cotswolds. I spent a month there in 88. Stayed in the Kings Head hotel. Lots of evidence of Roman occupation around the area. A Great place to see.