When you leave Portugal (or whatever Schengen country) to go back to the UK, the guards will stamp your passport with an exit stamp. Whether or not they actually bother to check when your entry stamp is - and then whether or not you overstayed - is not consistent.
I am a dual UK/EU passport holder who travels frequently between the two so I have some experience with this. A lot of the time, they just flip open a random page and stamp and that’s that. In some cases (for example the border at St Pancras Eurostar), the border guards will forensically analyse your passport for stamps.
If the Portuguese guards notice you overstayed, they have the discretion to fine you and ban you from Schengen for 5 years maybe. Or they might just roll their eyes and wave you through.
If you really don’t want to go back to the UK before your 90 days then just go to a non-Schengen country for a bit. Morocco and Gibraltar are right there.
Milan is bad but try Bologna where rental prices are now at Milan levels but which has more students, less housing and a recent tourism (AirBnB) surge. I got lucky, but I have student friends who were sleeping in tents in the forest for a while.