Not a particularly difficult job to set up, but I would have thought a 1/3HP motor was a little over the top for the job myself...
And of course you will need a fairly hefty PSU- 0-24V at 15A- available but not particularly cheap (about $175-200 Au or about 100 pounds)
The motor itself would be fairly large- this is a typical 24v 1/3hp motor in size (be aware that many 'elcheapo' brands are quite 'enthusiastic' in their ratings- to put it mildly...)
Specs
A 7" x 9" motor to run a 8mm chuck seems a 'little' large I would have thought???
A 0-24v 15A variable PSU (commonly available in various brands)
(this is from an Aussie supplier but I would think similar would be readily available in the UK)
A cheaper alternative might be 'thinking outside the box' and looking at electric bike motors- substantially cheaper, but you would need to step up in voltage though- most are 36 or 48v (again readily available), but you don't need a variable voltage one, as Ebike motors usually come with a speed controller (indeed while many have a 'twist' throttle', you can readily get 'foot throttles' as well but you might have to remove the chain drive cog that is usually fitted to put a belt pulley on (again, readily available)
This is one I have here that is going into a (old- VERY old lol) drillpress- its a 48v ebike motor that will run directly off my 48v battery bank (I'm offgrid running off solar) and cost considerably less than even the PSU alone above ($130 in total for the controller, pedal and motor, and an aluminium pulley to suit the belt drive on my drill) that motor is considerably cheaper, more powerful (almost excessively so in this case lol) than the one above... but again, it is a VERY powerful motor...
If you did use an ebike motor- then you would have the ultimate in portability- get a battery pack as well and run it 'anywhere' lol
;-)
(this is the drill press it is going to be in, currently in pieces, being rebuilt, that was when I first got it (it was literally being used as a garden ornament), but despite its appearance, is actually still in very good condition- years of sitting in a garden bed didn't do its appearance much good)