In order to secure a visa to enter the UK all applicants are police checked in their country of origin applicants are not let into the country if they have a
"conviction in any country including the United Kingdom of an offence which, if committed in the United Kingdom, is punishable with imprisonment for a term of 12 months or any greater punishment or, if committed outside the United Kingdom, would be so punishable if the conduct constituting the offence had occurred in the United Kingdom"
The only time this rule is not followed is
"save where the Immigration Officer is satisfied that admission would be justified for strong compassionate reasons"
This will tend to be in very extreme circumstances (i.e. for medical treatment, to visit a seriously ill relation etc.) and in these cases the visa granted would be likely to be very short term so it would probably not practically allow the individual to volunteer. Therefore any individual entering the UK on a visa for any significant length of time will almost definitely not have been convicted of a serious offence. If appropriate police checks can be done in the normal way to check if they have any police record for the time that they have been resident in the UK.
'Childcare organisations' recruiting volunteers to 'regulated positions' (under the definitions in the Protection of Children Act 1999 and Criminal Justice and Court Services Act 2000) are still obligated to check volunteers against the Protection of Children Act list (through a disclosure) even if they are from or have spent considerable time overseas.
Some countries (including most in the EU) have 'certificates of good conduct' or similar documents that citizens can request for employers but there is little consistency to the information they hold.
The Criminal Records Bureau has a 'faxback' facility for providing information on the appropriate authority in a limited number of countries to ask for criminal records information.
http://www.disclosure.gov.uk/