This comes up every year.

There are two reasons the BBC won't release the figures.

1, Because particularly in the early rounds and in the days it cost money to vote, they don't want people to know how relatively few the total number of votes are, compared with the viewing numbers.

2. They don't want a situation where a contestant may get very few votes compared with others. This could be embarrassing for that person, particularly if they've been putting in a lot of effort. It may also discourage people for signing up for the show, the following year.

It's a simple as that.

Any "manipulation," is restricted to the public perception of each contestant, generated by the judges' comments and selective training videos.
This can be quite influential.