Keep two basic facts in mind:
Nobody in London will care what the Iranian government declares your religion to be. Most people you encounter won't even have a way to know -- and those (if any) who can know also know that it is difficult or impossible for people considered Muslim by Islamic governments to change that categorization.
There are plenty of Muslims living in London -- about one eighth of the population self-identified as Muslim in the latest census. While some hate crimes do happen, it is not as if simply being (apparently) Muslim in London will automatically put you in urgent danger.
You can expect to meet some suspicion just for being a citizen of a country that is generally considered to be hostile to the west and often named as a state sponsor of terrorism. Your personal religious stance (or lack of same) does not factor appreciably into that. If you encounter questioning from authorities, your only option is generally to grin and bear it -- give honest answers and things should eventually sort themselves out.
Additionally, being a young man from the Middle East with weak ties to your home country (they must be weak, since you declare an intention to emigrate eventually) will make you look like an immigration risk, which can create trouble for you getting permission to enter the UK at all. Once you manage to get a visa, though, that hurdle will mostly be passed.