I am not an expert on where you might get the tooling in the UK but I can tell you what I use here in the US. But the tooling is not particularly special. A good tool supplier can provide most of what you need.
The big issue, as you have probably discovered, is to drill a long, straight, smooth hole through a 12-13" blank of hardwood. There are a variety of tactics you can employ to do that. We could spend some time talking about the pros and cons of some of those but it really is not worth writing a lot of words since the cons of most methods are considerable. But for the sake of letting you think things through I’ll mention the type of bits you could use. First is a spade/spoon/paddle bit on an extension which is cheap and very available. Next is a lamp auger which is a little more expesive and a little less common. Last is the gundrill which is a fairly expensive piece of kit.
The issue with the spade bits and auger are basically that the holes they drill are not always straight, smooth or of uniform diameter. They will wander as the grain and density of the exotoc hardwood varies. You can drill undersized holes and use multiple reaming passes to mitigate that. But the initial affordability of the drills is then offset by the cost of the various over/under reamers. But these will work fine enough if you are working on a wood lathe - if that’s what you have access to.
The reason a gundrill is attractive is that it will drill a long straight and smooth hole. That is what they are designed to do - and do it in hard metals. The downside is that you’ll want to use these on a machine lathe and it will need a long bed - at least twice the length of the blank you are drilling the hole through. That’s a big, expensive piece of gear. The gundrill is another hefty expense. These come from specialty suppliers like DrillMasters/Eldorado/Sterling and others. They can also be bought through eBay but may need to be re-sharpened. Industrial tooling supply companies will carry standard sizes and mounts. You might need a custom mount - depends on your set-up. The gundrill is meant to have cooling fluid run through it while you are drilling the hole. You won’t run fluid throug it while drilling wood but you will want to clear the dust using compressed air. For that you’ll want a compressor. It can be something small like a tire compressor - don’t need a lot of pressure or reserve volume. To connect that up there are a variety of methods too. Oh, and you’ll want a vac system to collect the dust as it leaves the blank. The dust from working exotic wood scan be quite harmful to your well being.
Method One -The drill can be mounted using an end mill holder on a Morse taper arbor in a tailpiece. Either the drill mount or the End mill holder needs to be modified to accept a nipple on to which you connect the air supply. I can provide some pics if you need them. You could do this on a wood lathe if you are hardcore.
Method Two - the gundrill is mounted in a quick change tool holder which means you have to have a quick change toolpost. In this case the air can be connected to the rear of the gundrill. I can probably find pics of that hookup too.
Now, no matter how you drill the blank, the end of the blank has to be free to be drilled into. This requires that you have some sort of commercial or DIY steadyrest available to secure the blank and to keep it rolling on center. This can be a set of rolling wheels or bearings or it can be a fixture with one large bearing. Again pictures may be needed to show you how that works.
Actually, if you take a look at Tyrone Head’s site, he has videos of the method he uses. That’d be a good place to look into how this is done and what you might need to do it.
No more words then. Everything Ty does is here: http://www.theflutemaker.com/tutorials.php the boring part is here: https://www.youtube.com/watch?v=RWz3pYKTrf8 Add up the cost of what’s in Ty’s shop and you’ll get pretty close to the high-end for what it takes to make a whistle.
To be fair here’s a lower cost example of how to do things. http://users.skynet.be/fluiten/how.html Yes, that’s a flute but the process is substantially similar for a whistle.
There are other ways that you might consider. Make the whistle in three pieces (a la O’Brien Rover). No long holes. You can use twist drills. You drill the pieces like you were making pens, just bigger blanks and drills, similar tooling though.
Or you can try the NAF method. Make the whistle in two halves. Route out half the bore from each piece and glue them together afterwards. Run a reamer through the bore to make sure it is centered and smooth.
So while you asked a simple question I am afraid that the answer is not so simple. I’d be happy to answer any questions that come up as you get deeper into this. It’s great fun to make your own whistles.
Hope that helps.
Feadoggie