Quality leather shoes with welted construction can be re-heeled and re-soled 3-5 times over their lifetime. Most owners don't take them to cobblers; they replace instead. Re-heeling typically costs £15-30; full re-soling £40-80.
When this is worth doing
Shoes with welted construction (Goodyear welt, Blake stitch). Upper still in good condition. Original price was £100+ (cobbler cost is proportionate to original quality).
Local cobblers across UK handle most repairs. Find one with good reputation; quality varies.