In reply to winhill:
I think the following is accurate. If anyone knows better, I'd be interested in hearing about it.
Most modern GSM phones you can buy in the UK recognise 999, 112 and 911 as emergency numbers. They might also recognise 000, 118, 119 and others. They then make a special emergency call, not a regular call to that number. In that case they don't even pass on the number you dialled, so it doesn't matter.
This has several advantages. The phone will roam to other networks to place the call. The network will pass some location information to the emergency services (in a city, it'll probably be very accurate, in the mountains it'll only give a very general area). The network will prioritise the call over normal traffic. The phone will likely make the call even if it's locked, or sometimes even without a SIM.
If you're phone doesn't recognise the number as a special one it will place a normal call to the number you dial. In the UK, 112 and 999 are absolutely identical, abroad you'll want to make sure it's the correct one.
The bit about texts is also useful. Googleing "text 112 uk" will likely get you no information, but there's a website here that might help
http://www.emergencysms.org.uk/
Finally, I'm sure everyone knows this, but it bears repeating: Mountain Rescue are not a service as far as the call centres handling 999 are concerned. When they ask which service you require, say police, then tell the police control room you need mountain rescue.