Upvote:4
You can ship your furniture at any time, regardless of your immigration status.
However, you may be required to pay import duties and taxes on your furniture, depending on the nature and value of the items. Reliefs are available, but there will be some paperwork involved to claim them. You might also be required to provide some security against the import taxes for the duration of your stay. It'll be this process that ties your import to your visa status.
The government notice that details the rules can be found here, and the shipping company will be able to provide advice too.
Note, though, that if you stay significantly longer than you declare on landing it can cause problems. If you declare a visit of, say, a month, and you stay for six then on your next visit the immigration officer will want to know how you supported yourself. If you can't present a watertight explanation then the officer may conclude you were working illegally and deny you entry. Be careful.