No, the rental you are living in would be treated as your Principle Private Residence. You have to take some basic steps to establish this with HMRC, which should include:
1) writing to them to tell them it is your PPR
2) ACTUALLY living in it. This means (at least) your mail should be going there.
However, as NJ pointed out, you can make nearly £11k of capital gain (and this would be the 20013/14 tax year now) in the tax year you sell it before any tax would actually be liable.