Hey man, welcome to the world of bass.
I've read your posts but only scanned the replies so apologies if I repeat the great advice that other members might have given. £300 is a sensible budget, and when I started out that was exactly the amount that I had to spend. I ended up buying a [b]Yamaha RBX170[/b] and an [b]Ashdown After Eight [/b]amp. I was lucky in that I had advice from a couple of musicians and, without it, I probably would have not gotten anything anywhere near as good.
I'd definitely [b]go used[/b] when buying your first bass. Not only do you get way more for your money, but you'll also get a lot more back if/when you decide to sell it (perhaps to fund something better ). Found a couple of basses [url="http://basschat.co.uk/topic/240632-modified-vintage-v4-icon-series-pics-added/"]here[/url], [url="http://basschat.co.uk/topic/239556-ibanez-sr370-4-string-bass-in-trans-blue-beautiful-cheap/"]here[/url], [url="http://basschat.co.uk/topic/231939-squier-silver-series-jazz-silly-price/"]here[/url] and [url="http://basschat.co.uk/topic/237452-bass-collection-sgc-nanyo-sb301-mij-upgraded-electrics/"]this bargain[/url].
With spending around £200 on a bass, you'll want something under £100 for your amplification. Amps at that price range don't vary too much, so it'll probably be best to go to GAK or Thomann or whoever's the cheapest and order a brand new one. If you can find a used practice amp that's good value, go for it, but there's not a huge selection in the 'For Sale' section at the moment.
Regarding accessories, go for the cheapest 'plug in' tuner you can find. Clip-on tuners are okay, but it's quite a faf and I wouldn't recommend using one unless you really have to. If you're buying used, [b]new strings[/b] are another purchase you might want to consider. The difference between rusty, dirty old strings and a new set is like night and day for experienced players, so imagine what it might be like for someone who is relatively new...