In the uk all votes are cast anonymously.
When you enter the polling station you identify yourself to the presiding officer, who checks that you are on the register. You are then given a ballot paper, on which you make your vote, and drop into the ballot box.
Other than the list of names There is no way of identifying you.
After the election the Electoral services officer will have a list of who has voted and who has not. This 'Marked Register' is only available to certain people - in general that means elected representative, registered political parties, and academic organisations. See page 38 of the document linked below for an accurate list.
The only thing the marked register shows is the fact that you have voted, not who you voted for.
The electoral register only shows your name, address, possibly age or date of birth (if you are coming of age during the life of that register) and the register number. It does not show you ethnic origin, religion, or any other information.
It is worth mentioning that the full register can also be requested by credit reference agencies, who use it for checking that you are resident at an address for financial purposes. They cannot get the marked register.
The issue of bme voters was in the news a little while ago. This link might be of interest