Looking again the the second photo, maybe a need a better quality bit. I haven't a clue what the bit's made of.Maybe a bit of lateral thinking - abandon that mounting point and use the upper one - or just keep drilling you seem to be doing ok by the second photo and if you haven't got a tap then nut n bolt it - me I'd be searching fleabay for an alternative frame "sorry dear it just wasn't repairable " hehe
Looking again the the second photo, maybe a need a better quality bit. I haven't a clue what the bit's made of.

This is my plan - thanks. Screwfix sells 5 Ebaeur 3mm bits for £4. The calipers deem the bolt diameter to be 4.8mm.Time to get some really good drill bits and cutting fluid (WD40 do some, and you'll easily get some at screwfix) - I think the reason you're not making any headway is because the drill bit is getting really hot and becoming dull very quickly. Some new drill bits and cutting fluid will work - the fluid will help keep the temperature of the drillbit down and make it last longer, but you'll still need to drill in short bursts and add more cutting fluid as you go and keep the drill at a low speed, it'll help you keep things straight and reduce heat build up. Use a narrow drillbit first and then widen the hole out as you go.
Perfect, couldn't ask for more!An unexpected bonus is that the threads appear undamaged as the new mudguards are now firmly in place.