Actually, it does make one and only one important difference: There is no check on your government passing laws that restrict your rights. For example, Heller simply cannot happen in the UK. Yes, you do have many of the same “rights” as we in the states. However, you also don’t have a strong right to self defense, reasonable expectation of privacy (all those cameras), right to bear arms, etc. In other words, your government can and has simply voted out of existence many of your rights with simple laws. This is all the more ironic in light of the Magna Carta...
And this is different from the US how exactly?