I'm not sure about letting agents, but I don't think you'll find a 3-bedroom apartment in London for £375 per month (or do you mean £375 per person per month - so about £1,100 a month for the whole property).
I'd imagine that you'd be looking at something more like a minimum £375 per week for 3 bedrooms in London - doing a quick Google search for 3-bedroom flats in those areas, most of the results are about £400-£1500 per week, so £1,600-£6,000 a month for the whole apartment (Notting Hill and Whitechapel are more expensive, but Camden Town, Bethnal Green and Shoreditch seem to be closer to the £300-£500 a week mark).