Sounds like you're referring to netbooks, not notebooks. A notebook is just another word for a standard sized laptop.
It really sounds like you need a proper laptop. Netbooks are designed for little more than browsing the net (hence the name) and tablets are nothing more than toys.
You're in the UK, so I cannot really help you find a specific model, but you should look at ~13 inch laptops. They do exist, and they're usually vastly superior to netbooks. Make sure they have anything besides intel graphics if you want to do any gaming. Pretty much any AMD or nvidia graphics chip will be better.
If you end up with one without an optical drive, you can always use your desktop to rip the DVDs to the hard drive, then transfer them to the laptop. I've already done this for my entire collection, blu-rays included. I use a programs called makemkv
for blu-rays, and a program called handbrake
for DVDs. This is especially useful if you use media center as a DVR as I do.