112 is supplemented in France with 15 (Medical) and 17 (Police) emergency numbers.
USA, Canada, Mexico = 911; Aus = 000 (112 from mobiles) NZ = 111
A full alphabetical listing, of national emergency numbers by country is at Wikipedia here
At the bottom of this page there is a comprehensive listing of the non urgent contact numbers for the UK's different police forces, including how to phone them from abroad.
Consular assistance if arrested abroad - website only with drop down search facility for specific resources by country
Consular and other UK government offices abroad - website only with extensive links list
NHS Abroad. It would seem NHS advice for UK people overseas is fairly limited. This page on the NHS site offers advice on healthcare services and the EHIC (European Health) card by country. This page is the standard NHS symptom checker site, where no phone call is needed.
Alternative non-emergency contact numbers by police force:
(From Police.UK at 25 June 2014)| Police force | Telephone number | From abroad |
|---|---|---|
| Avon and Somerset Constabulary | 01275 818340 | +44 1275 818340 |
| Bedfordshire Police | 01234 841212 | +44 1234 841212 |
| British Transport Police | 0800 405040 | - |
| Cambridgeshire Constabulary | 01480 456111 | +44 1480 456111 |
| Cheshire Constabulary | 01244 350000 | +44 1244 350000 |
| City of London Police | 020 7601 2222 | +44 20 7601 2222 |
| Cleveland Police | 01642 326326 | +44 1642 326326 |
| Cumbria Constabulary | 0845 3300247 | - |
| Derbyshire Constabulary | 0345 1233333 | - |
| Devon & Cornwall Police | 01392 420320 | +44 1392 420320 |
| Dorset Police | 01202 222222 | +44 1202 222222 |
| Durham Constabulary | 0345 6060365 | - |
| Dyfed Powys Police | 01267 222020 | +44 1267 222020 |
| Essex Police | 01245 491491 | +44 1245 491491 |
| Gloucestershire Constabulary | 01452 726920 | +44 1452 726920 |
| Greater Manchester Police | 0161 872 5050 | +44 161 872 5050 |
| Gwent Police | 01633 838111 | +44 1633 838111 |
| Hampshire Constabulary | 01962 841534 | +44 1962 841534 |
| Hertfordshire Constabulary | 01707 354000 | +44 1707 354000 |
| Humberside Police | 01482 597600 | +44 1482 597600 |
| Kent Police | 01622 690690 | +44 1622 690690 |
| Lancashire Constabulary | 01772 614444 | +44 1772 614444 |
| Leicestershire Police | 0116 222 2222 | +44 116 222 2222 |
| Lincolnshire Police | 01522 532222 | +44 1522 532222 |
| Merseyside Police | 0151 709 6010 | +44 151 709 6010 |
| Metropolitan Police Service | 020 7230 1212 | +44 20 7230 1212 |
| Norfolk Constabulary | 01953 424242 | +44 1953 424242 |
| North Yorkshire Police | 01904 618691 | +44 1904 618691 |
| Northamptonshire Police | 03000 111 222 | - |
| Northumbria Police | 01661 872555 | +44 1661 872555 |
| North Wales Police | 0300 330 0101 | - |
| Nottinghamshire Police | 0115 967 0999 | +44 115 967 0999 |
| Police Scotland | 01786 289070 | +44 1786 289070 |
| Police Service of Northern Ireland | 028 9065 0222 | +44 28 9065 0222 |
| South Wales Police | 01656 655555 | +44 1656 655555 |
| South Yorkshire Police | 0114 2202020 | +44 114 2202020 |
| Staffordshire Police | 0300 123 4455 | - |
| Suffolk Constabulary | 01473 613500 | +44 1473 613500 |
| Surrey Police | 01483 571212 | +44 1483 571212 |
| Sussex Police | 01273 475432 | +44 1273 475432 |
| Thames Valley Police | 01865 841148 | +44 1865 841148 |
| Warwickshire Police | 01926 415000 | +44 1926 415000 |
| West Mercia Police | 0300 333 3000 | - |
| West Midlands Police | 0345 113 5000 | - |
| West Yorkshire Police | 01924 375 222 | +44 1924 375 222 |
| Wiltshire Police | 01380 735 735 | +44 1380 735 735 |
End (of this post - suggestions for improvement welcome)
