Better Integrated Amp?

You really should look into the Parasound Z series. You can get separates, an amp, preamp, and phono stage for less than a grand if you shop carefully. You have to pick a pair of speakers first though. A little backwards to buy an amplifier system and then speaks IMO. 

I am somewhat confused.

So you have a TT right?   And the cost of that, I believe was 350,  is to be included in the 1000 pound budget. If correct, you have 650 left.

You have a modest sized room so need to be thinking about speakers that are easy to drive such that they can be driven by 50-100wpc integrated amplifier. The higher the speaker sensitivity and the impedance the lower the power needed. 

Is the Yamaha A-S501 (as mentioned by others) available to you? It has an internal phonostage and DAC. Should be around 350 pounds (sells for $550 in US).

This leaves 300 pounds for speakers. 

Now, If you are willing to save money over the next year or two to upgrade speakers you could purchase a low price pair now to get you into music with an opportunity to search for the best pair to compliment your system and tastes. Just one approach. If you have found speakers you like but put you over budget, find a used integrated to drive them with the idea you can upgrade it later. 

The speakers are the component that'll give life (or not) to your music... it is crucial that you find a pair that suits your taste BEFORE buying an amplifier... BTW, you are lucky... UK has many great electronic company, as Tannoy (speakers), Rega (turntables), Sugden (amplifiers), Spendors (speakers) and many many others... If you are willing to buy used, you could basicly double your purchase power... good luck with that!

Okay based on what all of you’ve said I think I may be able to stretch my budget a little bit, probably only a few hundred pounds extra but it might make a difference. I’ve also found a website which offers massive savings when you buy an amp and speaker set together which is looking like a really good option for getter better equipment affordably.
The speakers that this bundle and extra cash opens me up to are: Q Acoustics 3050i, Dali Oberon 5, Wharfedale Diamond 12.4, Yamaha NS-F350, Fyne Audio F303, KEF Q550 and BowerWilkins 603. Amp wise I could choose between a few but the two that stand out are Marantz PM6007 and Yamaha A-S501. Like you guys have said though, I’ll disregard picking one for now until the speaker side is sorted.
This seems to be a significant improvement on my previous options and at a very small change in price, what do you guys think?
Speaker wise I haven’t been able to look at all in detail just yet, I’ve heard good things about the Dalis, the 603s are the most expensive to buy separately but obviously that’s not always an indicator of quality - I haven’t looked too deeply into these yet - and Wharfedale and KEF seem to be a strong brand name. The website also says that I can request quotes for other speakers they have listed as part of a speaker amp deal but these seem to be the top speakers there.

If there is a way, check Monitor Audio. They often offer good performance for relatively little money. They are serious brand, too and are originaly from UK, i think.