Hi
The National Archives has a searchable database here
http://www.nationalarchives.gov.uk/records/looking-for-person/divorce.htmFrom experience, not everyone who claimed they were divorced actually were.
From chatting with the people at the Divorce registry in London, many couples get around to having a decree nisi but then don't go back to court 6 weeks later to have this made absolute, so aren't in fact legally divorced.
I know this may not seem palatable but William Gibson was born in Derby, married in Scotland and remarried in the Wirral, as he seems to have moved around a bit it might have be easy for him to say he was divorced when he wasn't.
You can also make an application to the courts for a decree absolute search
https://www.gov.uk/copy-decree-absolute-final-orderIt's expensive at £65 for a 10 year search and there may not be a decree to find after all.
If there is a decree, all you'll get is a A4 copy of the date and place they married, then the date and place they were divorced. You won't get any case files.
Dawn