Are aluminium wheels worth upgrading to “better” aluminium wheels?

I certainly noticed the improvement swapping between Fulcrum Racing 5 (winter) and Fulcrum Racing 3s (summer), so why not buy a second hand pair of 3s to use for 'best' and keep the 4s for winter? Shouldn't cost more than £200 if you're patient - even for the more recent ones with the wider (c17) rims.

When I swapped out some worn Zondas for Calimas, I noticed the downgrade. It follows that an upgrade would be similarly noticeable.

....don't know about deep section carbon wheels, especially cheap ones.  You might be better with a decent set of alloy wheels than cheap carbon wheels, many of which are way ove 1500g and have poor rim braking surfaces.   

I have a couple of pairs of sub 1500g alloy wheel sets (Mavic Open Pro UST and Kinlin 22s on decent hubs - Chris King and DT Swiss 240s both tubeless - and a set of Shamals .... I had to spend GBP 1800 to get better what are arguably better  carbon wheels. 

I think the question is what are you wanting to gain ? A few seconds off your Strava times,more comfortable ride,wheel stiffness ? If you've ever done group rides then you'll see that the person first to the top of the hill is probably not on the high end wheels. I would run the wheels you have and enjoy the bike while not getting too hung up on Strava times.

You'll only notice any substantial benefit by going deeper and carbon. Be aware that you'll need to change your brake pads, and depending on the rim you choose your braking distances may be lengthened somewhat. I've got ~10 year old Bora wheels that are... lethargic when it comes to slowing down. They since profiled the brake track with little bumps and the new Bora wheels brake better than my alloy rims do

I'm with the others, Fulcrum Racing 4's are pretty decent alloy wheels and a different set of alloy wheels would make at most a very small improvement which will be barely noticeable. 

I would however say that a depeer set of carbon wheels which is also lighter would make a noticable difference, especially when riding at high speeds. I'd advise getting them from a good wheelbuilder such as Wheelsmith, Cycle Clinic or DCR Wheels whose base level carbon wheels are really not much more expensive then the alloy wheels you've listed. A wheelbuilder will also give you a much better warranty than off the shelf wheels which could save you money in the long term.

Light Bicycle from China are also another option and they have a very good reputation, I know of several people with Light Bicycle wheels who love them and the company are nothing like the dodgy eBay sellers we've all seen about. However, if there were any issues then you would have to send them back to China which is certainly offputting for me. 

As you say, Fulcrum Racing 4s are actually pretty good value wheels. Whilst not exactly high-end wheels, they are decent all-rounders and already significantly better than the unbranded stock wheels you get with many entry level road bikes. As such, I don't think upgrading them now makes a huge amount of sense - I don't think the improvement in performance will be noticeable enough to justify the cost.

Being rim brake, they will need replacing eventually anyway - you could always consider going up a level at that point.

You can get carbon wheels from UK builders for ~£600 without resorting to far east sellers (that can be somewhat pot luck).

I've personally used Mark Pollard (https://www.spokesmanwheels.co.uk/) for a couple of sets, one alloy, one carbon.  Good, solid, no nonsense wheels and substantially better than any value wheels (previously I had Kysrium Elites).  Obviously his website could use a little work(!), but he's solid and pretty quick.

38mm carbon, £585, 50mm carbon, £650.  I speced DT Swiss hubs on mine so they were a bit more expensive, but they're very true, have taken substantial abuse and there is a very noticeable performance advantage.

Obviously other builders exist, but the point remains that you can get very good carbon wheels substantially cheaper than the Hunts and Zipps of this world which are not far off your stated budget.

By changing wheels, what gains are you hoping to make?

In my opinion I'd save your money and concentrate on increasing your fitness, while decreasing your weight, neither of which you have mentioned, but both far more relevant to going further, faster, than any spangly new wheels.