Stereo speakers are going to sound substantially better than any £150 soundbar for TV. They'll knock on the door of soundbars at £300+ for TV, and they'll pee all over far more expensive soundbars for music. However £150 is a bit thin to get all the bits you'll need for TV sound with a stereo amp and speakers.
To get a working solution you'll need
(1) a stereo amp with remote control - The cheaper proper stereo amps don't have this as standard.
(2) some way of getting a digital signal (via optical) from the TV and into an amp that has (in most cases) just analogue stereo inputs on the red and white connections. [At this point you might be saying "But my TV has the red and white connections!"... if it does then 999 times out of 1000 they're 'sound going in' sockets when what the TV needs is 'sound coming out' sockets. Connecting to these will do diddly-squat and you'll end up having to buy an optical to analogue converter in the end so let's cut to the chase
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(3) speakers and speaker cable... and possibly something for the speakers to stand on
We could put together the components with some entry-level product that fits the bill.......
Pioneer A20 amp (with remote) @ £150 + Optical to analogue converter (Ebay or the rain forest) @ £15-£25 + Optical and analogue stereo cables - say £10
or... just go for the Monitor Audio A100 (£150 on clearance) which is a stereo amp with optical input and IR remote and Airplay and Network streaming too... oh, and a What HiFi 5 star review. Add an optical cable for a fiver and that's the amplification all sorted.
Now, speakers...
The go-to budget option is generally the Wharfedale Diamond 9.0. They're usually daft cheap for the performance they give (£59) but at the moment they're obscenely cheap at under £40 a pair. As good as they are though, personally I'd spend a little more because the performance goes up a lot. Either Tannoy Mercury V1 (£69/pr) or Q Acoustics 2010i (£79) is where I'd put my money. They have better bass and I think a clearer midrange. IMO well worth the extra few quid as a long term investment.
Speaker cable doesn't need to be anything fancy. Just get something pure copper and of a decent thickness. A 49 stand with a cross sectional area of 1.5mm will do just fine for runs up to 10m per side.