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Sorry if it is one external wall I was interpreting your plan.
Even with one cold wall if you are generating steam it is unlikely that any extraction system will be able to remove the vapour fast enough to stop a proportion of of the vapour condensing on the wall and generating mould and damp. Replacement air for the air extracted will need to come from somewhere if it is outside then it will be cold and also maybe damp. All I was saying was look at your alternatives before spending £200 on core drilling. Have you looked at reducing the steam you shower makes by choosing a different shower head also could put a bigger radiator in the bathroom would cost more in fuel bills but you might still spend less than £400 over 20 years. -
Look at insulating the external wall with Marmox multiboard .
@Silly_Savage you seem to be addressing the symptom and not the problem and spending a lot of money to do it. The reason you have a problem in that bathroom is that you have three external walls which if the building is Victorian are probably 9" solid brick (so no need for specialist core driller) which provides little or no insulation. You need to address this before spending lots on extractor fans. Also if you are replacing the window go for triple glazed wood Rationel do excellent ones