Guess what OP, you are expected to tell customs/police/council you're here for more than 3 months (90 days) and therefore register as a temporary Swiss resident, they'll then expect you to import as a migrant resident even temporarily your effects including your car (even if for less than one year in total).
Then if you're story doesn't match between the Police, Council and Customs ....expect fines. They communicate with each other (with your passport number as reference).
The critical question is are you staying more than 3 months but less than a year?
If so then you can import your UK car for a year and keep your UK license, insurance, tax, MOT, emissions etc but you must fill out a form @ customs and get an exemption. Otherwise they'll apply CH rules and you'll start getting invoices and compliance notices under local rules.
Did you get a receipt of your application for a residence permit when you went to the Police/Gemeinde? You'll need a copy of this to re-import your car legally once registered. The clock will then start from this date. Under exceptional circumstances it's possible to extend the waiver for the vehicle for up to 2 years and keep UK plates, MOT etc.
However you will need a Swiss motorway vignette to drive on the motorway each year regardless. In addition you'll need to exchange your EU license for a Swiss one before being here a year to be allowed to continue to drive. (If you think that's bad you would only have 6 months in Germany moving there from here).
The exception is if you're working for a special status employer like the BIS, UN etc. where you don't qualify as a full resident in any case and therefore have a special i permit (eg Li, Bi, Ci).
Go to www.ch.ch
for more info in english. www.bs.ch
has some english info too for new arrivals.