You do not need a visa. You can stay in the UK under the Immigration (European Economic Area) Regulations 2016, even though Switzerland isn't part of the EEA, thanks to an agreement between Switzerland and the EU.
This means that as long as you are working or studying or can prove that you are self sufficient you can stay for longer than three months. You can apply for a registration certificate to show that you've demonstrated this to the UK authorities, but it's not necessary. For most purposes, your Swiss passport or ID card will suffice.
The UK's public information page concerning this is at https://www.gov.uk/eea-registration-certificate.
I don't think that volunteering counts as working (but I'm not sure; it might), but a part time job does, so that's a possibility. The self-sufficiency route would also be appropriate.
If you're self sufficient (or a student), you should consider getting "comprehensive sickness insurance."
This is of course very likely to change when the UK leaves the EU, or possibly at some point thereafter. Another thing to consider is that the UK seems to be making life difficult for people who are in the country under these regulations, which might tip the scales in favor of trying to stay under the radar rather than applying for a registration certificate.
Most questions related to such an arrangement belong on Expatriates.