If an engine doesn't start using the POH procedure, get it serviced!
The fuel servo may be knackered and needs an overhaul.
For example, my engine - while starting as per the book every time - used to really shudder on shutdown. Nobody thought it was abnormal. However, when it recently went to the USA for the SB569 crank swap, the firm noticed this and said it wasn't right, and they found a leak in some fuel control valve in the fuel servo; it wasn't closing properly and some fuel was getting through, preventing a clean shutdown. Now it's fine. But nobody in the UK would have noticed this.
That fuel servo would not have been looked at until overhaul @ 2000hrs which for most private pilots is "never". And even then I doubt the usual UK engine shop would have noticed anything.
The thing which also helps hugely is the installation of the new Skytec lightweight starter. I got the latest
NL model fitted. This is a lot more efficient because the permanent magnet has been replaced with a wound magnet; it rotates the engine several times faster than the stock starter, making cold starts instant and hot starts sorted within 2-3 seconds.