Better Integrated Amp?

You seem set on a TT for your first system.  Is there any reason for this?  Do you have a  collection of records already?  If not you have to add the cost of vinyl into your budget.  Not inexpensive these days unless you like older music and scour the used record stores.  

If you have your heart set on vinyl that's great.  But, you might want to start off with an integrated and decent speakers first for your budget.  Can you use your phone or computer for music?  Do this and then save up for a DAC, phono stage, and TT.  I paid $200 for a used Gram amp 2 phono stage and it sounds pretty darn good with my vintage Dual TT that I spent $150 on (plus another $160 to get it up and running perfectly).  

Actually, check out the Iotavx sa3 which is pretty well regarded and comes with a DAC and phono stage built in.  Then look at Triangle BRO3 or one of the Klipsch or Elac bookshelfs.  For less than 1k you can have a nice rig.  Maybe even have enough left over for a decent vintage TT!

Best of luck

"...check out the Iotavx sa3 which is pretty well regarded..."

This reads too good to be true. Really full package including dimming all the lights on the faceplate.

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!