Ouside lighting - can you tap off a feed from a 3a fused spur inside house to run a 400w lamp?

Basically yes as long as the work complies with building regs/BS7671.

If your planning on doing DIY electrical work in the home, you need to apply to your local authority and pay to obtain Part P building regulation consent. Once consent has been obtained you can then start work. Failure to comply with the regulations can result in a £5000 fine. Ideally lighting should be on its own circuit, but a 3amp fused spur from a sockets circuit would be acceptable. The spur itself should be of the RCD type (unless the existing circuit is already RCD protected). Maybe best to hire a Part P registered electrician as its far easier and cheaper than applying for consent from your local authority. Google Part P building regulations for more information.

Yes a 3 amp fused spur would be absolutely fiend or that type of light

Hi Practically yes it can be done, technically and legally you should be a qualified electrician to do it. hope this helps