You’ll have wasted heat under the kitchen units
That's not really a problem as it's a constant temperature system - not constant power. So while things will be warmer underneath units, the actual power will be minimal.
I don’t imagine running an electrical cable in a heated floor is a fantastic idea, how do we rate the cable that need to be used, I would look for an alternative solution
How would you rate a cable for any other installation that didn't run at 20˚C ambient ? Typically a wet UFH will be limited, both by a thermostatic valve, and in my brother's place an over-temp cutout on the manifold as well.
So realistically, your cable is going to be at an ambient of around 30-35˚C max, which from a very vague recollection is going to require a derating factor in the order of 0.5.
As others have already pointed out, the "tricky bit" will be digging a chase without damaging the pipe - though in-situ pipe repairs are possible if it's needed. However, I strongly suspect that almost all kitchen fitters and electricians will consider this in the "far too difficult, just tell the customer it's impossible" category. It's not, just very difficult - they won't be able to just whizz the chase cutter across as many will have become used to.
At one time, digging out chases was something given to the apprentice or junior (going back even further, drilling holes to fix sockets/switches with the "revolutionary" Rawl drill was also given to the lowest in the pecking order) - and for good reason. These days the apprentice or junior seems to have been replaced with the chase cutter - not that I'd have given this job to an apprentice (except perhaps the bulk bits between, and not close to, the pipes) ...
So first thing to do will be to locate the pipes. When I helped a mate out with renovations a few years back, I took a load of photos, including with measuring tapes in place, which I gave to him so that in the future there needn't be any guesswork as to where the wires are under his bathroom floor. I rather suspect that few installers do that, and if they do, the house owner doesn't realise their value and they don't get passed on to the next owner. Luckily when I bought our current house, the previous owner still had a "partial" set of architect and structural engineer drawings - though sometimes, on the "ignorance is bliss" approach, I sometimes think I might have been better without
As mentioned above, a half-decent thermal IR camera should be able to locate the pipes. You'll need to let the slab cool for a while (sticks finger in air and guess, perhaps several days). After that, you turn on the heating full whack and watch the camera. It may take minutes, it may take hours, depending how deep the pipes are and floor construction - but you should be able to see hot lines appear and mark them on the floor.
When you have a good idea of pipe location, and with the acceptance that there's no guarantee you won't damage any pipes, you start chasing by hand - carefully. If you are quite sure where the pipes are then you can knock out in between them quite quickly, but as you get closer you need to be more and more careful.
At first, you'll be working as if the next blow in the chisel could put it through a pipe - and this could go on for a while as you won't know how deep they are. But you may get some clues while doing between the pipes - e.g. finding the top of the insulation or boundary between main raft and screed. Once you've found the first pipe, you'll have a better idea - but you can't assume they'll all be at the same depth.
This probably sounds time consuming - it will be
And the bill will match that unless you elect to do the long slow hours yourself.
Oh yes, it may well be a good idea to isolate the UFH while you are doing this
Having found the pipes, you then decide whether to take the cable over the top of them (if they are deep), or (also really carefully) tunnel under them if they are shallow.
There is the option of running a conduit into which a cable is drawn, or just concreting the cable in place. There are pros and cons both ways. I'm a conduit whenever I can sort of person as I like to be able to replace cables if they get damaged or requirements change. I'm just finishing up in our lounge, and the previous owner who built the extension just clipped the cables to the walls and plastered over them. That meant digging out what seemed like miles of chase to free up cables I wanted to move
But you need more space, and it slightly lowers the current carrying capacity of the cable.
And if you get all this work done, consider if there's anything else you might want at that island - you've just done all the hard work, right ? Though I would point out that a drain for a sink will be impossible (or at least very impractical) given that there are so many other constraints with a drain.
And have the UFH pipes well pressure tested before reinstating the floor - if there's a weak spot you want to know about it now while it's relatively easy to deal with ...
So, in summary :
Contrary to what you have been told, it may well be possible to have both your island and keep the UFH.
Not a lot of trades will care enough to even consider that it's possible.
It's not going to be cheap, and it's not going to be quick.
You may have to "positively rebut" a number of explanations why it's "impossible". Most of these will translate into "too much hassle and I don't want to do it" - or worse, "I'm rubbish and my job and I can't do it" (in which case, find someone who can).
You'll probably need several trades - especially I wouldn't allow most plumbers or kitchen fitters anywhere near electrics.
That probably raises more questions than it answers ...
Simon