I wouldn't, I've heard the weather forecast from Friday onwards - its going to get a lot colder with lots of overnight frosts, so wait till that all passes first. Then when you do want to put it outside in a different pot, you'll need to harden if off first by leaving it outside during the day for extending periods over a few days till its been out all night on, preferably, a mild night.

It's a Passiflora caerulea (blue passion flower). This is the hardiest passion vine and will grow outdoors and it will survive UK winters.

I would leave it in the pot until next month then unravel the vine from the loop, put it in a pot or into the ground and train the vine around a trellis, arbor or fence. You will probably end up with about 10 - 12 feet of vine when in is spread out. Be careful when handling the vine, it's easy to snap it or crease when you unravel it.

About 10 years ago I bought one in a pot similar to yours from a garden centre. I planted in a large pot and trained it around my conservatory. It grew very well, but I was sick of clearing the dead leaves up and I got rid of it. When I did I gave a neighbour a cutting and it's now covering virtually the whole side of their house, albeit south facing. The flowers smell absolutely wonderful and they sometimes fruit.