As in all things, consider an extreme - you wouldn't be able to keep water warm in a 1mm pipe, but in a 1m pipe you'd have trouble changing it.
Cooling effect of environment is proportional to
(surface area divided by volume).
= (length * pi * diameter) /(length * pi * diam *diam /4)
Ignore the 4, as we're just looking for proportionality and you get
1/(diameter)
So eg if you need 25mm insulation for 15mm pipe you only need
(15/22) * 25 = 17mm for 22mm pipe
Which is somewhere the Water Regs Byelaw 49W35 figures of 25mm for 15mm pipe and 19mm for 22mm pipe.
I was wrong about the costs though, now that copper is more expensive. The extra cost of the insulation for 15mm is about (1.60- 1.05=) 55p per metre (prices from
screwfix)
whereas 22mm tube cost about £1 per metre more.
Insulation figures vary by 2 :1 for best:worst materials.
Best figures are 0.020 W/mK or better (lower!)