Unfortunately, I'm too new a player to answer that from my own limited stock of experience, but here's a compressed version what the Strategy Guide says about what affects other civs attitude towards you:
1. Prior positive negotiations. (In other words, how fair you were
with them in the past).
2. Honouring treaties. (Ratting on them and to some extent others too, has an effect).
3. War (naturally!)
4. Culture. (Higher culture improves everybody's overall opinion of you)
5. Military strength (yeah, they get more respectful towards the strong guy in the game too.)
6. Scientific achievements. (Apparently you get nicer treatment if you are significantly ahead of them).
I'm sure that I've also read somewhere that establishing a trade relationship with a country builds friendly relations - even to the point of giving them gifts (but I don't know how well or how quickly this works). I have read posts where people spoke of giving away crappy cities that they'd captured, or were having problems with, and that the receiver was thrilled! But I've never tried it out - I always bring my cities around.
Like most things in this game I think that there's probably not always an instant fix and it's a matter of slow accumulation. Your situation with the English probably won't change much just through time passing, it will need actions from you to rebuild it. Perhaps looking at something you have spare (an extra luxury or something) and asking them what they would offer you for it (often better than just demanding a price) might be a way to start?
Good luck. Hope this helps.
