'Just' 10ml ? Not much chance of that......
Haha yeah... the 'only' part was relative to the amount of blood in your body
I've been on a mild dose of beta-blockers (80mg Propranolol) before, and needed bloods taken whilst I was in hospital and nobody could draw any blood because it caused my blood pressure was to go too low. Several staff could hit several sites but nothing would ever come out. And I'm a young, fit and healthy male who's never used needles, so I can only imagine how hard it may be to draw blood from someone who's been injecting for a while.
Steering back on topic. If the on-call doctor fails to draw blood after several attempts and finally renders it futile, then the police have four main options:
1) If you only look a tad squiffy and are no real cause of concern to them, they can detain you for up to 24h and then just release you without charge.
2) If you look moderately squiffy and are a cause of concern to them, but they don't think that marching you to hospital will be worthwhile, then they may change the Section 5 charge (Driving Under the Influence) to a Section 4 charge (Dangerous Driving). Their only headache in doing that, is that S.4 (Dangerous Driving) will be harder to prove because they will not have any evidence available to indicate that you were driving dangerously due to being intoxicated by drink/drugs, so they'll have to resort to other evidence that may not prove beyond reasonable doubt that you were driving dangerously.
3) If you look moderately squiffy and are a cause of concern to them, but they don't think that marching you to hospital will be worthwhile, and they also don't think that they have sufficient alternative evidence to charge you with S.4 (Dangerous Driving) instead of S.5 (Driving Under the Influence), then they may reduce the original Section 5 (Driving Under the Influence) charge to a lesser Section 3 charge of Careless Driving (aka Driving Without Due Care & Attention), because it carries a much lower burden of proof than S.4 (Dangerous Driving). The difference being that for a successful S.4 (Dangerous Driving) conviction, they would have to prove beyond reasonable doubt that (1) 'your driving fell far below the standard that could be expected of a competent and careful driver', and that (2) 'such driving was obviously dangerous to a competent and careful driver.' However, with the lesser S.3 (Careless Driving) charge, the lower burden of proof means they only have to demonstrate that (1) 'your driving fell below the standard expected of a competent and careful driver.'
4) If you look highly squiffy and are a real cause of concern to them, then they will in fact march you to hospital in the hope that the better facilities and more specialised staff on duty will provide them with a better chance of obtaining bloods for evidence, which also gives the police the opportunity to have the hospital provide you with any relevant medical attention if necessary.