There are "better" receivers than your JVC, but probably not so much better that it would make a big difference.
However, your speakers have a quite low sensitivity; in other words, they need more power to achieve the same loudness as compared to speakers with higher sensitivity. This means that you will run out of power more quickly, if/when you want to be able to play them loud, at least on occasion.
You are unlikely to ever push more than 40 watts (the JVC's rated output into an 8 ohm load) into your KEF speakers on a sustained basis, but at higher volumes and/or in a larger room, you may not have enough power to deliver transient peaks in the music. When this happens, the amplifier clips (distorts) the signal. A little clipping is usually no big deal, but any more than that and the distortion will become noticeable. On a related note, a heavily clipping amp can, somewhat paradoxically, deliver more power to the tweeters and midrange drivers than they are designed to handle. Also, significant clipping can trigger some amplifiers to oscillate, which in turn can cause damage to the amp and, potentially, the speakers.
Peaks in a good recording can be 12-15 decibels louder than the average volume level, or even more. A 12dB peak demands 16 times more power, and a 15dB peak demands 32 times more power! So, for example, if your JVC is running at a steady 2 watts - which would give you around 80dB of loudness at a listening distance of 10-12 feet on a continuous basis - a 15dB peak would demand 64 watts...and would result in a bit of clipping distortion. BTW, 80dB is what I would consider only a bit above a moderate volume level.
Bottom line, you seem to like how your JVC sounds with your KEF speakers. As long as you aren't trying to play them LOUD, and/or if your listening distance is closer and/or your room is relatively small, 40 watts may well be just fine. As a point of comparison, I have a set of speakers with the same sensitivity as your KEFs, and I run them with a 170 watt amp. That probably seems like a huge difference, but in reality only provides 6dB of headroom vs your JVC.
If you do think about moving to an amp with more power, I would recommend at least doubling what you've got. Doubling the power provides only 3dB of additional loudness (or headroom for transients). 3dB is not a big change; it is defined as the smallest change as to be easily apparent to a person with average hearing.
Another reason to consider a different amplifier, in addition to available power, is sound quality. Generally, higher end integrated amps and separates (separate preamp and power amp) offer better sound quality than receivers. However, especially in the world of vintage gear, integrated amps may be pretty much identical in design and sound quality to their receiver siblings (other than not having a tuner built-in). Also, note that not all "separates" are better than all receivers.
If you go down this path, I would urge you to limit your consideration to amplifiers rated to handle 4 ohm loads. Your KEF's are a very easy load to drive; they don't drop much below 6 ohms at any point in their frequency range. But you may well end up with more difficult-to-drive speakers in the future. For example, many modern bookshelf speakers are rated at 4 ohms, and drop well below that at various frequencies. It can be difficult to determine an amplifier's abilities into a low impedance load, but one good clue can be the difference between its 8 ohm and 4 ohm power ratings. Look for a 4 ohm rating that's at least 140% of its 8-ohm rating...more is better.
The last thing I would mention is that the crossover capacitors used in your KEF speakers were not as high of a quality as used in KEF's upper tier speakers. This, plus the facts that electrolytic capacitors degrade with age and your speakers are getting close to 45 years old, might make replacing them (the capacitors) a good idea. This has the potential of providing a fairly significant improvement in sound quality, and would be a more economical first step vs stepping up to a higher quality, higher-power amplifier.
EDIT: I noticed that you posted the same thread in two different forums. This is against the rules here. You can use the "REPORT" button at the lower left of your post to request a moderator to delete one of them. I would suggest deleting the one in the "Member Systems" forum.