I buy/take the bags from certain airports which do them slightly bigger than others, reuse for a dozen flights or so. I travel a lot.
I second the Primark kit. The equivalent of Boots where I live also has them.
In one bag I can fit one each of shampoo, conditioner, face wash, perfume, roll-on deodorant, BB cream, contact lenses liquid, anti-bac, hand cream and toothpaste. Some bottles are smaller than others (70-100ml) so I pack them non-consecutively IYSWIM.
All throughout the year I save hand cream and toothpaste tubs that are almost empty (eg still have 4-5 days in them) and those are the ones I use for travel.
If going somewhere for over a week, I buy generic supermarket shampoo, deodorant and toothpaste once there.
If you're cheeky enough at security, you place your (loose) coat right next to your liquids. This way you may avoid having to close the zip or seal the bag and can take more through. I couldn't fit all of the above in a sealed bag. An open one, yes. I'm probably 'caught' 10% of the time so worth the risk for me. You need to look confident and like you know what you're doing and they won't touch the stuff on your tray, just push it along. Security staff are thankful when somebody knows the deal and is in and out of their spot in less than half a minute.