Perfectly lawful here in the UK, as long as the load is properly secured. But in practice - I think I mentioned this earlier in the thread - to be safe, particularly when filtering through lines of traffice, the item being carried needs to be no wider than the handlebars. That way the 'cat's whiskers' principle applies. If the bars will go through, the rest of the bike, with sax, will go through too. The bars on my bike are 96cm wide, and a tenor case is typically around 80cm, so that leaves a little leeway.