I also found that ‘coombe’ means a steep valley, so I suspect you're right. Everything seems to point towards English roots.
On the site below, you can search country of origin based on immigration records. Although not many are cited, it seems England is the source. As to the age of the name, I guess you'd have to research when and how surnames arose in England.
My guess from looking at the UK distribution of this name (again from the below site) is that it arose in the countryside. Just thinking logically, I would suppose that more urban folks would use last names that referred to occupations i.e. butcher, baker, wheeler, etc. and those from the country would use surnames based on location. Especially as people migrated from countryside to city.
http://www.ancestry.com/learn/facts/fact.aspx?&fid=10&ln=griscom&fn=