Primary school starts in the year the child turns 7. So kids born in 1999 start school this August, 2006. There are primary schools that teach in English in Helsinki, Vantaa and Espoo. They are state schools and therefore free (with the exception of the International School of Helsinki which charges approx 12 k euro per child per year). However you child would have to be a fluent English speaker to be accepted as there are admission tests. These schools teach the Finnish national curriculum in English, they do not offer English foreign language. The English School in Helsinki is in a slightly different category, it does take children who do not speak English.
http://www.eschool.edu.hel.fi/index.html
If you are staying in Finland long term then I suggest immersion, bilingual schooling where the children start off in English and then gradually do more and more Finnish. There are also integration programmes for immigrant children.
http://www.minedu.fi
There is a search engine on the above site where you can find details for all the lower comprehensive (grades 1-6) schools in Helsinki.
I'm no expert on primary schools in Helsinki but I have 2 kids (3rd and 6th grade) in Espoo international school (English language teaching) and one in 7th grade at Kulosaari school (also English language schooling) in Helsinki. Would be happy to answer your questions.... Can't help much with pre-school but there are quite a few English language pre-schools in Helsinki so getting in to one shouldn't be a problem. If you have a KELA card you should qualify for a state subsidy for pre-school education but I'm not sure about the amounts and the criteria.
I'm sure you'll get some more posts after the bank holiday weekend...