I can recommend the
Linx 10 in tablet for £149. Someone recemended them to me a few weeks ago and I bought one and love it.
It runs full Windows 8.1, so you can run any programs your PC can, you're not restricted to apps from an app store. It has a micro SD card slot to simply and cheaply expand the storage. I'm not into games but you can get a
proper X Box controller and plug it into the USB port(that video is the 8 inch version) and play proper games. The Linx has a micro USB but comes with an adaptor to plug in standard size USB stuff.
There are some good unofficial Youtube apps that let you download and save videos, without ads, so you can watch them even without network access, like on a car journey. And you can install BBC iPlayer of course.
Don't know how old your kids are but as they grow this is a proper PC and can run Word, Excel, Powerpoint, OneNote and Outlook etc and comes with a one year subscription to Office 365 which includes those so they can do proper homework etc with it. You can plug in any USB wired or wireless keyboard/mouse or get a bluetooth keyboard and mouse.
I'd stick with Windows 8.1. You can upgrade free to W10 but IMHO W10 isn't as good on a tablet as W8.1. I am going to restore my Linx back to 8.1. MS may tweek 10 and if they add back all the swipe gestures that 8.1 has for tablet use I may go back. You have until at least July 2016 to upgrade free. I didn't like Windows 8 on my PC but on a tablet it works really well.
Negatives: The speakers are not that powerful, but perfectly okay. A full size USB socket would have been nice. IE has a nice tablet UI but is a bit slow, but you can of course install Chrome or Firefox. Chrome actually has some of the swipe gestures that Windows 10 took away, like swiping from the left to go back a page.
Edit: Again depending on how old they are you can create user accounts and
parental controls to restrict what they can do if you want. You could create an Admin account for you and a User account for them so they can't run certain programs or restrict how many hours a day they can use it etc.