Please note that pull factors in immigration do not have anything to do with the country from which the immigrants are coming. The factors that make them want to leave their own country are push factors. This means you could have push factors that led British people to leave the UK and go the US. However, the pull factors are specific only to the US. The pull factors that drew immigrants to the US between 1820 and 1850 are the same for immigrants from all countries.
There were three main pull factors that made the US attractive to potential immigrants. One of these pull factors was freedom. The United States had a democratic system of government where essentially all white men got to vote in meaningful elections. The US also had a system in which people’s rights, like the right to freedom of speech and religion, were respected. These are potent pull factors.
The other two pull factors were economic, and can perhaps be seen as just one pull factor. This factor was economic opportunity. We can split this (as the link below does) into economic opportunity and plentiful land, but we can also say that these are both forms of economic opportunity. In short, the United States had a growing economy and it had plenty of land. This meant that people could find lots of opportunity in the US, both if they wanted to do some sort of work in a city and if they wanted to farm for themselves.
Thus, political and personal freedoms as well as economic opportunities constitute the pull factors that drew immigrants to the US between 1820 and 1850.