I was a part-time student, managing on typically no more than 5 hours total a week, especially towards the end of my nearly 6 years of part-time study. I spent 3 of those years writing up. I had a false start and had to restart the writing after a year, to get the right voice, approach etc. If you have a full day and some extra time I think you should be fine. But make sure you are clear about keeping that time. You need to put in the hours regularly, week after week. And it is a long slog. More of a marathon than a sprint. But it's doable.
It's also possible to do it in really short bursts. I did most of my writing up in 1 hour chunks. I had a clear idea of what each chapter would be about. Then I would pick the 2 most appealing chapters, and work on those simultaneously (I get bored doing just 1 at a time). And I would draw up to-do lists of what I needed to be getting on with in each chapter - really easy low-level breakdowns - and then I would pick the most appealing, or least unappealing. And that way I made progress, even in short bursts.
It would help if you have an idea of when you will be submitting, and can then work out a timetable for when the different chapters will be finished. Let your supervisors have a copy of this, and then stick to it. That's what I did, and it kept me motivated and moving onwards.
Good luck!