If you want to get involved in the local community, meet people or have a skill you would like to offer, you might consider volunteering at one of the many local charities or community groups active in Oxford. Although volunteering is unpaid, some opportunities offer skills training or managerial experience which can be valuable on your CV (resumé).
You can find more information about volunteering on the UK government website, or search the Do-it database of volunteering opportunities. The University Newcomers' Club run regular sessions on volunteering and publicise opportunies through their email lists.
If you have a visa with a restriction on any work, do check if this might be a problem and read through the government website.