I think all three of my knockabout bikes could be contenders. Since 2000 I've kept a cheap runabout for commuting, trips into town and those wet/winter weather rides I don't want to subject the good bike to. So, the nominations are:
Apollo Meltdown - Bought new for £100 plus the cost of mudguards and a lock. It was heavy, paintwork became tatty in no time flat, seat clamp broke so that it would randomly tip the rider off backwards. It did however survive 3 years of regular commuting and another couple of years of off road trips before it became uneconomical to repair.
Apollo Excel - I visited
Halfords to cost up replacement parts to fix the Meltdown. My calculation got it to at least £80 for parts or there was the Excel on offer for £60. No brainer I thought

. Again it was heavy (an anchor might be an alternative use for it), slow (I never got better than 11mph average out of it) it was full suspension (the front was very stiffly sprung while the back bounced around like a happy dog), the geometry made it feel like riding a clown bike and the brakes fell apart (no, really fell apart). It did however last five years before wearing out, including rides in the snow and a number of rides over the Long Mynd.
Hawk Trakatak - I picked this because after the last one I just wanted a basic bike I could have fun tinkering with and upgrading when parts wore out. It's heavy, but the geometry suits me and once the supplied tyres were changed I found it quite nice to ride for a cheap bike.
Unfortunately this one didn't have the build quality of the Apollos: the back wheel started snapping spokes the summer after I got it, the pedals snapped in half lengthways

, the stem broke, the seat clamp broke and ...., well it might be easier to list the parts I haven't replaced yet.
Rather sooner than expected I've had my fun tinkering and upgrading and I've turned it into a fairly decent bike which, on a good day isn't very much slower than my best bike and has taken me on some properly adventurous rides.
And the winner is....... The Apollo Excel, for being the heaviest, most uncomfortable, slowest and bounciest bike I've ever been stubborn enough to keep riding: