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My question concerns the use of “which”, when not preceded by a comma.

I have recently encountered objections to sentences such as: "This is the house which Jack built."

I have seen it alleged that such a sentence (containing no comma after "house") can only correctly be written as: "This is the house that Jack built."

I have no objection to the sentence "This is the house that Jack built." Is there anything grammatically incorrect about "This is the house which Jack built." (I realise that the latter form is not normally used in the USA but I believe it is correct in the UK.)

Please advise.

Thanks.
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this is something the grammar checker on Microsoft Word always stresses over in my writing - I IGNORE the dictatorial Yanqui machine and use things the way I want to -

apparently Americans get taught this rule at school, but we don't in the UK!
Comments  
'That' is restrictive, that is, it tells you a necessary piece of information about its antecedent:

- This is the house that Jack built.

While 'which' is non-restrictive.

- I live in that house, which Jack built.
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 suzi's reply was promoted to an answer.
I'm sorry for acting like a dictatorial Yankee machine. Just ignore me.
LOL
no offence intended!

in fact - I have posted this question several times myself, on a linguists' board, and was ignored. I was prompted to ask because of Microsoft word's grammar check - presumably they ignored me because it is so common-place to US-writers ; the "experts" did not believe my problem!
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