Better Integrated Amp?

What is the rest of your system? 

Considerations:
   Budget
   Speaker sensitivity and impedance.
   Room size.
   Loudness levels.
   Use of digital as well as vinyl.

I would focus on auditioning speakers 1st, and consider the amps that are paired with them during audition. 

What budget are you considering for speakers? 

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.