How much do you have to spend?

If you spend the majority of money on your speakers & choose a pair that are fairly sensitive & easy to drive (minus extreme impedance & phase swings) you can get away with spending much less on surrounding equipment while getting great results. 

Upgrading to the KEF 1's is a legitimate upgrade. Even objectively they are superior & should give you instantaneous perceivably differences from your LS50's. 

Personally I would also focus on acquiring an integrated that works in the analog domain only. Separate your digital & analog components. Low noise components. An external Dac & external DSP for the subs. The LS50's do have their limits though..I can understand wanting to trying something legitimately better. 

If you are on a budget, used gear from a reputable dealer rather than an online dealer. Buy products that can be serviced in your area. Buy speakers with easy to get and replace spare parts. Start with digital only with a nice internal DAC, live Bluesound or Eversolo. Stay away from Turntables, it is absolutely a money pit, consumes to much time. Don’t stretch yourself budget with that nonsense. You need a solid state integrated amplifier which has an internal DAC, like Hegel. Cables has many reasonable great options new or used, even from Amazon. Speaker selection is the most important. You need go to few dealers and audition them, go to events like Axpona or Audiofest which help to to discover which interpretation of sound by each speaker you like. After $3000 for a pair speakers, all speakers sounds great. Beyond that price, it is an acquired taste for that interpretation of the music by speakers. Speakers and amplifiers are the most important components. Stick to Class A of AB amplifiers. Tubes are not for starters and costly. For front end, Garbage in garbage out doesn’t apply to digital front end. If you focus on digital front end only, you can have a great system below 10K$ budget. 

Fritzenheimer

After $10,000 to $15,000, it is all diminishing returns until the room is treated.....IMO. The room is easily the equivalent to going next tier on: preamp, amp, DAC, transport, and cables.

I was NEVER a room treatment believer until about 2 years ago, when I took my current gear over to my friend Patrick's house after he had just had his room treated with GIK solutions. Similar size room, similar power upgrades, only difference was a well though out treated room.

My gear I used at the time was about a $19,000 set (preamp, amp, DAC, Streamer, Speakers), but in the several days of  listening in Patrick's treated room and playing with speaker placement; I would have thought it was a completely new system......maybe $35,000.

That taught me enough, that I  embarked on my own project. I am finishing my basement by adding an extra bedroom, bathroom, and completely from scratch dedicated audio room......should be completed and ready to install gear by beginning of June. Giddy up!

I had nine years of music lessons - played in orchestras, concert bands, jazz bands and rock bands.  So I think I'm at or close to golden ears.  My system is; 

Magnepan 3.7i's with Magna Risers stands (highly recommended)

Conrad Johnson MF2500 solid state power amp 

Paramount Halo P5 pre-mp

Technics SL-1500C turnBtable 

Marantz UD7007 SACD/Blu-Ray player 

I dont understand how people can think that the gear pieces choice matter more than basic acoustics knowledge.

The right question is not how much are you willing to spend for which brand named gear...

It is how much time it will takes to learn mechanical,electrical,acoustical ,DSP optimization process... Knowledge of acoustics being the most important with basic concepts and their real time perception in a room .