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Sorry, forgot to reply to this. I realise I am a bit lost, I thought active/powered speakers (like the ones you linked to) don't need an amp, or possibly come with a dedicated one in a third box?
I am trying to save space so really want smallest reasonable option.
chez_jay-
active/powered speakers don't need an amp
You're right. What I meant was use "normal" hifi passive speakers with an amp like this: https://www.amazon.co.uk/dp/B00SATAEEA/ref=psdc_3030841_t1_B00OR5OBFY
My thought process was that to get bass and mids you inevitably need a large speaker. Computer set ups usually do this by having a separate sub with the tweeters near your ears.
Those amps are pretty small and can be screwed into stuff if needed. So I was thinking that a small or medium sized bookshelf speaker with an amp that can be flexibly and discretely located - under/on the side of a desk, shelf, etc. might net you less space, or more usable space on a budget.
However, there probably is an OTP option much more suited.
hugo7
Possibly not the suggestion you're after, but I'd prob get a mini amp and then try some cheap small speakers you like the look of / size of. There will be load of 2nd hand choices and they can be easily changed if you want something different.
these will prob go over your budget, but you may as well add them to you watch list in case:
https://www.ebay.co.uk/itm/Audioengine-A5-High-Gloss-White-Premium-Active-Powered-Speakers-Pair/283600674849?hash=item4207eae021:g:cdMAAOSwpDRda5Z2