I entered and left the UK four times in the last two months so I can tell you my experience.
When you arrive the UK Border Force wants to know how long your stay is in the UK. Every time you enter you will go through Immigration and get a stamp. Your days outside the UK are not put on the landing card. Only that current stay.
So, if you do a journey of 50 days UK, 10 days paris, 20 days UK, in that order, you would put 50 days on your first landing card. They will probably ask you where you plan to go afterwards. Just be honest. When you return to the UK, using the above example, you will then put 20 days on your landing card.
They don't care about the number of days of your entire trip unless they ask. Only the time in the UK. And only the time of that current stay. (While you see it all as one trip, they see it as two separate visits to the UK.)
And for my four stays, even with one being one night, I got four stamps in my passport. (In fact, the two I got at Heathrow were by the same officer. ) The other two were Edinburgh and Paris-Nord.
The address you should provide is the one you will be going to that first night.
I have stayed in 14 different hotels in the UK and Europe over the last two months and have never been asked where I was going next or what hotel I would be staying in. The only thing the hotels all asked for was my credit card.