Perhaps having a writing space doesn't matter. I'd argue in fact that having a writing routine matters a whole lot more. It doesn't have to be a big writing space to leave enough room to create a great work of fiction. A laptop or a table and notebook is enough. But what is more important is a routine. It doesn't have to look the same every day, but if there are writing routines built into your week, you know you will get to your writing regularly and it will get done. This is far superior to having a room dedicated to writing. A room will only get you in your space, facing the wall. The routine is what will get your writing going.
3 Ways you can make the most of whatever space you have by establishing your routine:
1. Make it realistic
You may have to cut some things out of your schedule to fit in the writing you want to be doing. If you had a lot of free time already you'd probably have tackled the projects that are important to you. By making space in your calendar and booking in your writing time like appointments, you are shaping up your day to realistically achieve your goals. Note: If you front load your day with your new writing time, you are more likely to get the writing work done. New habits call for new routines. If you still find you have creative energy left over at day's end and want to do something besides binge watch Netflix, by all means put in another session. But don't count on late night to be a consistent production source. It doesn't happen for most people.
2. Decide on an outcome you want to achieve
Whether you want to write a certain number of words on your novel per day or blog several times a week, decide on an outcome you want to achieve. Whatever it is, the person it is most important to, is you. Unless you are on staff for a magazine or blogging for a company, you will not have outside expectations. Personal projects and visions require more discipline. Deciding on what will look like success in your writing time in terms of output means you know when you are achieving it because it's a matter of looking at the word count and posting frequency. Looking with a critical eye on the results too early can result in project paralysis. In comparison, the routine system examines process, not results. Focusing on process increases practice and that in turn improves the writing and grows the readership which is what you were after all along.
3. Attach a deadline
In order to build accountability into your personal project, attach a deadline and inform some people who care about your success. Let them know when they can read your post, first draft, contest entry, etc. Put it on the calendar and meet up and produce the work. Alternately, saving time over meeting up in person, there are many writer's forums and online groups in which you can post deadlines and share work for feedback. Take advantage of them or create your own. It is by utilizing these micro deadlines that you will achieve the project you've been dreaming of.
So yes, a space is nice, but it is not essential. What is critical to your writing success is to establish a routine for getting your writing done. With it in place, all you have to do is execute.