Is there a good/bad time of year to change your accommodation?

So, I’m in my apartment the literal size of a car park space, walking distance to the job, in a rent-control city. I’ve been here for two years, and while it was a step up from the claustrophobia of my parent’s, and is exceptionally cheap, I find my health is affected by days staying at home. It’s the same four walls and no ability to sleep at night in the same room, and the lack of movement means the weight is creeping on. I’m in my mid thirties & sharing is not an option. I need what I had in Canada for the same price, a 1 bed with a living space and bathroom attached. I’ll pay the premium that my permanent job can give me, but it will involve moving out of here to the parent’s for a time, saving up the deposit, and then I can start the hunt after 3-5 weeks.

The question is, is there a time of year I need to avoid doing this at? I’m looking at the ads now & so many are student accommodation in the off-season. Should I race the students for accommodation in September, or wait till their rush is over and start looking in October-November?