My advice - don't worry about the pickup right now. Buy the best acoustic guitar you can afford, stick generally with Dreadnought styles for the lower end you are looking for.

Add the pickup in later - easy enough to do. Buy a clip-on tuner for the headstock (lots of offerings under $30 these days) and forget about the built-in tuner.

For an add-in pickup that's almost effortless to install, go with an LR Baggs I-Beam. It will sound much better than what you will get in knock-off guitars. Save up around 120 quid and you're there with an eBay purchase.

It's hard to know what brands are for sale in the UK in the lower end of things (which seems where your price point is).

-Scott