Bosch Multi Material Drill bits, available from Screwfix.
http://www.screwfix.com/c/tools/drilling/cat5920002#category=cat5920044&brand=bosch
Don't waste your money on solid carbide, without a drill press you will break bits. Even with a press you may break bits. Don't waste your time and money searching for Cobalt. The Cobalt HSS is only slightly better than regular HSS and whatever bit you get needs to be well ground. Unless you are shopping at Cromwell or similar industrial supply place, chances are the drill bits won't be all that well ground. I have used Cobalt on both hard and soft steel and didn't find it was worth it on the hard stuff. The Universal bits scrape with a sharp edge, rather than cut, but they are tough, cheap, and forgiving if you don't hold them dead straight since they are carbide brazed to a slightly smaller steel body. They won't be dead accurate, but good enough and better than some ways.
Interestingly, this thing, a spade type solid carbide for hard steel has a cutting edge a lot like those universal drills.
http://www.drill-service.co.uk/Product.asp?Parent=020480020000&Tool=355 Good source for drills, but overkill for this job.
Whatever you do, do not drill pilot holes and then chase down them with larger drills trying to enlarge the hole. This is often repeated advice, and sort of works, but it makes for inaccurate holes and tends to trash the drill. Twist drills require the centre of the hole they are creating to keep them centred. Drill in a pilot hole and get shake and vibration and out of round hole. If the difference between pilot and final hole is too small, the bigger drill won't cut and just rubs its way down, then breaks. If you drill into a pilot hole the bigger drill encounters a sharp corner at the pilot hole edge and chances are it will chip. I have broken and damaged too many solid carbide twist drills, while in a press, attempting to enlarge holes in harden tangs to think its even remotely a good idea.
Filing will be painful. You can try a chainsaw file, but its not going to be fun and won't do the file much good. The only way I have found to do this for a nearly right size hole is a 1/8" solid carbide burr in a rotary tool (Dremel), running fast. Carbide burrs likes speed. Unless the hole being enlarged is only slightly too small its hard to keep it round with this.
Use a chunk of steel underneath the tang, clamp it so that you can lean on your drill, drill through into the support block. The block will help cool the work. The only thing that drills hot is Stellite, everything else is better cool. That's why industry spends so much on spray cooling and cutting fluids. The support block also helps control break out and gives a cleaner hole. Does not need to be hard steel, some mild will do. Aluminium will too, but steel would be better in this case.
The local softening method with a torch can work, depends what the blade is made from. Not too much danger to the blade temper if you keep the blade wet. However it is possible for steel to be soft and still be horrible because of how the carbides are distributed, and the torch is only going to temper the steel, not take it back to full soft. Can be worth trying, but if it doesn't work, there are always those Universal bits
Good luck!