You can get 50mm TCT core bits, which are designed to be used with an SDS drill, quite cheaply, but any core bit requires a lot more torque than the average DIY drills puts out - unless you have one of those 750 to 1200 watt monsters, in which case you might be OK. If not you will need to either beg, borrow, hire or buy an SDS drill. Core bits ideally need to be run at low speed, but the 750 to 900 rpm a lot of SDS drills run at should be OK with a 50mm core
If you do buy an SDS, go for one with rotation stop as that means you can use it for light chiselling, chasing and breaking work in the future. An SDS will make drilling walls and concrete floors a breeze and if you do a lot you will really appreciate the addition to your tool kit (and how fast it drills holes in masonry). I'm not a fan of those big cheap 5kg Titan (and other) SDS drills - maybe that's because I'm a wimp, maybe it's because i drill too many holes above waist height and I just find them ridiculously heavy (great if you need to take lots of stuff out at lower levels, though0
For your 50mm holes start by drilling through all the way with a long pilot bit, then drill in from either side of the wall using the core bit's pilot in the hole as a guide. This will avoid the blow-out which often occurs with a core drilled straight through from one side only. You will need to stop the drill from time to time, withdraw the bit from the wall and clear the waste (small cold chisel or plugging chisel and a hammer will help) before recommencing drilling - this is because the drill isn't deep enough to hold half the thickness of the wall
I fitted a number of kitchens this way with an SDS drill and a TCT core before buying a dry diamond core set and a dry diamond core drill. The TCT bits don't cut as fast, but they are a lot cheaper, which is especially important if you aren't doing loads of holes. I still do the odd bit of coring out for people - at £20 to £30 a hole depending on the number and size of holes, so bear that in mind (when you butter 'er indoors up to try to get the dosh for an SDS)
