Reply #7: BE CAREFUL about the time of day, though

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I've hauled luggage through London tube stations at rush hour on a few occassions, and I can say that you probably don't want to be doing this at a busy time of day.

Worse comes to worse, take a black cab from Trafalgar to Victoria station. It may be a few £££s extra, but it will definitely be worth the headache prevention.

Once you get to Victoria, take the BR train to Gatwick. Last time I was there it was ±£7-- but this was ten years ago now. Either way, it's your best bet to Gatwick.