Our 3 year old Westie normally sleeps in the kitchen at night with the door closed. She would regularly scratch the door at around 3am to try to join us in bedroom. We therefore left the door open, but closed a glass door between the kitchen and bedrooms(bungalow). She now does not make any more noise, but every morning there is a puddle by the glass door and she is back in her basket. Despite scolding she is persisting in "protest" peeing. Note that she has peed in the garden at 10pm.
Can anyone give any advice?

Scolding after the event won't help as she won't understand why she is being told off, they just don't add 2+2 together like we do.
She is a small dog and they have little bladders some may find it hard to get through the night our yorkie needs to go about every 5 hours so cannot quite make it through the night so we use an old towel we can wash out in the morning for him to use rather than get up at 2am to let him out. If you can get up that may be a better answer but it's purely what is most convenient to you.

Move her bed into the bedroom so that she is in the same room as you? I understand not allowing dogs up on beds etc, but if you put her own bed somewhere in the bedroom you may well find that she is altogether more contented and might stop peeing indoors.

I don't think she is sitting in the kitchen each night planning which ways to wind you up and deciding that a good old 'protest pee' each night is the way to go, they don't work that way. Maybe the dog has compared your 'scolding' with the wee and sees it as bad so goes when you are not around?? Scolding is wrong and means nothing to the dog but to fear you. When the dog goes out for their last walk/toilet break bedfore bedtime is there anything in the garden like an old plant pot etc they may be drinking from in excess that is filled with rain for eg? Also when you see the dog weeing outside, praise and treat her so she forgets this 'scolding' now. Has she always slept in the kitchen with the door shut? Maybe she is trying to let you know she wants out but you cannot hear? A visit to the vet might not be a bad thing as well to rule out infection if you think it is totally out of character.

You give her attention when she pees on the floor.

Therein lies your problem.

If its by the door, then I would assume she's been trying to get out to go, but couldn't

I have a Yorkie, which is about the same size as your dog, and he wakes me up most nights to be let out for a wee..if one the odd occasion he can't wake me up, his accidents are always right by the back door, where he has tried to get out..I would never scold him for it though, because its my fault for not waking up, and I know he wouldn't do it on purpose

My dogs have a dog flap open at night into a secure garden. Tilly sleeps downstairs by choice as she likes to be on cat watch but Bailey sleeps with me and he has to get up some nights but he just goes out does a wee and comes straight back to bed and snuggles back down with me.