I think you could argue this.... Maybe ring Citizens Advice and explain the situation, see what they say. Its not like you kicked the fence over, it blew over from strong wind, which makes me think it wasn't to secure to begin with. Also, read your tenancy agreement. Generally for fixtures and fitings, home owners are responsible. Hubs used this as example, say a tile fell off the roof, then the roof leaked. That would be the landlords responsibility. But if you went on the roof and damaged the tile, then the roof leaked, it would be your responsibility.
How about checking with the owner first, then if they are not willing to fix it, try Citizens Advice?