A lot of misunderstanding and confusion in a lot of these comments. I am am medical student in the UK (not a Muslim though). Hope I can set a few things straight.
Some people here have commented "I hope they catch the disease" or similar. A large percentage of medical staff ARE colonised by MRSA, but that doesnt mean they'll "catch" anything. Similarly, C.diff is not going to bother anyone but those who have had their gut flora cleared out by antibiotics.
The evidence base for going bare-below-the-elbows is actually slim to none. There are almost no trials comparing infection rates with this policy and without, and no particular evidence that sleeves cause infections. The policy is a department of health initiative to make them look good at fighting HAIs.
It IS however reasonable to assume that sleeves can spread infection, but it isnt really much more than that, an assumption. I of course comply religiously (if you'll pardon the pun) with the guidelines, because its part of my professional behaviour. If I wasnt doing it, I doubt anyone would bring it up, but if I wasnt washing my hands, they sure as hell would. I see a LOT of senior staff not complying with this, because they're hearing feedback from their patients that short-sleeves and no ties (the other part of this guideline) make them look scruffy. I'd say the staff that comply with it MOST are nurses (which had it as part of their uniform years ago), medical students and junior doctors.
A lot of people too aren't really understanding the concept = its not just in theatre, but in day-to-day ward practice this is necessary. However, it is also worth noting that there are many medical careers that are suitable for low amounts of clinic contact and might be easy to apply a strict muslim dress code. Those that say they should "find another career" - debatable. I would be very slow to say that to someone. There is ALREADY room in medicine for people to refuse to perform a procedure that interferes with their beleifs IF 1) it does not put the patient at risk and 2) you can quickly direct them to a colleague of equal skill who CAN. This is already used day-to-day with women's health, abortion and so on. Spreading infection DOES put patients at risk, but there ARE ways of adapting dress code to help this. Its not as simple as "bare arms or get out".
Oh, and for everyone who mentions the hippocratic oath, its NOT a requirement for practicing doctors in this country and very few have taken it. Some (and increasingly many now) medical schools do include a "pledge of duty" or similar in their graduation ceremonies which acts a little like a modern version of the HO though.
