Passive speakers need an external amplifier, whereas active speakers have the amplifier built in to one of the speakers. Better quality studio monitor speakers have an amplifier in each speaker.
For £100, Edifier's are a very good choice. There are some low budget studio monitor speakers for similar money, but it seems that a few too many corners have been cut to meet a certain price point with some of them. M-Audio AV42 are pretty good though, although even they aren't quite a good as their AV40 predecessors.
Passive speakers and a small T amp, is another option. Wharfedale 9.0 and either a Topping or SMSL amp is a good combination for about £100.
All have 4" woofers and will certainly be larger than the Logitech's you were using, so best to check you'll have room.