“I was going to do the washing, but we would run out of washing powder.” Shouldn't this be “but I thought we would”?The question is about...

The consideration of " href="http://www.bbc.co.uk/worldservice/learningenglish/grammar/learnit/learnitv213.shtml">the
future seen from the past" isn't effected by the inclusion of a phrase
indicating someone's mental contemplations. When standing alone, the clause "we would
run out of washing powder" is an assertion: a positive statement given without
corroborating fact. You can add, "I thought," making a speculative statement:
conjectural thought. You can add, "I concluded," making a deductive statement: a
conclusion based upon knowledge. You can also add "he thought" or "she concluded," or
"they asserted." None of these affect the combined tenses used when speaking in the
present of things that occurred in the past and involve something that would happen in
what was yet the future at that time: you or someone else can be assertive or
speculative or contemplative or thoughtful or deductive in a past event that involves
something yet to happen in the future at that time.

To
illustrate, imagine you are talking in 2011 about something that happened in 2009 and
involved an event yet to occur in 2010. You can add assertion or speculation or anything
else and nothing regarding the tense will be affected because all parts relayed in your
2011 communication already happened in the past. This imaginary illustration also
explains why you can know that the future element did happen when you say something
like, "In April, they left Edinburgh on Tuesday expecting they would arrive in Amsterdam
on Wednesday." You can know they arrived because both parts of the sentence are now in
the past (unless someone adds, "But catastrophe struck!"): You are speaking from your
present vantage point (perhaps July?) about two things that happened in the past in
April, though the second part was in the future (Wednesday) when the first part occurred
(Tuesday). In other words, after they left on Tuesday, Wednesday had not yet occurred
and you are talking in the present about both that occurred sometime in the
past.