By letting NOW do all the leg work. Don't cancel the current provider, let NOW sort this out.
Call the broadband team.
NOW Broadband Members can call us 8am–8pm, 7 days a week.
I made the move away from Plusnet to Now.
If you have done this right, then you would have signed up to Now without telling plusnet you are leaving or cancelling ( this is important)
Plusnet will send you some emails along the lines of sorry you are leaving sometimes with a few offers to tempt you to stay, you may also get a letter in the post ( i did) from plusnet with similar stuff to try and make you stay with plusnet.
At some point your now router will arrive, it will have a go live date on it - usually a sticker on the box that will tie into your go live date from Now.
The evening before my go live date i re-configured my router ( which is my own not one form plusnet or now) If you are using plusnets router and will be switching to the Now box the same step would be to unplug the Plusnet router the night before and plug in the now router .
The following morning the broadband had switched to Now and all was up and running
This was roughly 14 days from ordering Now, if you are "out of contract " with plusnet, plusnets final bill should be equal to the amount of time before you switched to now, if you are in contract then you will be charged for the remainder of your minimum term.
If you have completed the steps in the correct order the change should happen overnight.
If not then you could face some down time, and at worse you may be on a significantly slower connection if your local open reach cabinet is full.
Tip: before you go live with now, and when you have the router you can configure the now router before connecting it to the phone line, use an ethernet cable to connect to the now router and change its SSID ( wifi name) and wifi password to the same that your Plusnet router uses and keep a note of it, also keep a note of the now router passwords as you will need these if you need to re-set the now router at any point.
If the now router has the same wifi name and password as your old plusnet router then when you switch it over all your devices should connect with out having to go to each device and change its wifi settings ( odds on there will be more than you think)
@chilli2 is right, that is exactly how it should happen. Unfortunately it doesn't always go as it should.
If PlusNet should make an offer that matches now, take it. If not at least give them a ring to see if they will offer to match, but do not cancel. Say you will think about it, and then let the transfer take its course.
Hope it works out for you.