Don't panic, most agencies will ask for a group of people because it makes life a lot easier for them, it can be difficult finding individual students and guessing whether they will get on or not. However, there are landlords out there who will accept single students. And also during June-August, there are always rooms available in shared houses. for instance, a 4 bedroom house is occupied by only a group of 3.
If your looking for a more homely feel, I would recommend that you go into a house with no more than 4 bedrooms, they are generally medium size and feel more cosy and give of a good atmosphere.
Look at the letting agencies in Plymouth, and just email/telephone them all explaining your situation .. there will be someone who will get back to you!
There is one letting agency I would recommend that you avoid though.. there called Shoreys (Apologies to TSR if this is not allowed!) I had a bad experience with them in my first year. I had to into a shared house because i was ineligible for halls, so I said I wanted to share with first years preferably and they said that they will only put people together who they believed would get on, and over the summer they kept informing me of the people who would be living in the same house(telling me positive things about these people of course)
Eventually I agreed on the property... When I moved in , I was faced with 8 people, 4 of the guys were Rugby/Football players and they were just HORRIBLE NASTY people with no manners or respect .. im a 5ft 2 timid girl who bounced into the letting agency in a flowery dress and these were the people they thought I would get along with.. At one point we had to get the police involved due to harrasment both verbally and physically from these guys.(1 Guy was arrested, the others got a warning). We just wanted to get out of the house because we were actually scared to live there and the agency just wouldn't let us leave despite the guys breaking their contract themselves.