Here in the U.S. one can either hire a professional "stump grinder" at about $50 (USD) per stump or a local DIY rental store will rent a serviceable unit, if you can tow it home, for about $80 per 8 hour day or $45 per 4 hour day. Either way, it would take about 30 minutes to remove the stump down to a level of perhaps 2 feet or so below the surface of the ground. It will also provide you with a wealth of chipped wood for mulching plants.. I'd assume the same is available in the U.K.
You don't say what kind or how big your stump is. Some. like Ash or Maple can have roots ten feet down, while others, including most evergreens are much shallower. Regardless, unless it's under 6 to 10 inches in diameter, it's going to be a job...
Dig them out - its the only way - my hubby has dug 4 stumps out of garden - then there is the problem of disposing of them - it took my hubby and 2 neighbours to lift one out of the hole.
get gorrot, from a good gardening out let, drill or cut a hole in the top centre, pore in the gorrot, and leave, in the mean time as it works, (rotting throught to the roots, ) place around it pots of flowers ect, to hide itm ok