Full info on how voting in TV shows works, from the BBC Strictly website's "About" section:
I have been trying to vote, but keep getting the engaged tone.
Because the phonelines are very active throughout the UK when the vote window opens, some callers may experience the engaged tone - especially those in rural/remote areas. We recommend that you call back within a couple of minutes when the traffic through your local exchange would have subsided. Engaged tones are controlled at local telephone exchange and something that the BBC cannot control.
I called but received a dead tone.
If after dialling the first four numbers of the premium rate number you heard a dead tone - then this means that you are premium rate barred and you should check with your network operator about lifting the ban if you wish to vote in Strictly Come Dancing.
I tried voting, but couldn't get through. Why?
Given the high volume of viewers and callers that some TV voting shows generate, it is possible for a very large number of people to pick up the phone simultaneously when the onscreen announcement is made. Sometimes this can cause some callers to get an engaged tone for short periods of time immediately after an onscreen announcement; however, any congestion tends to clear quite quickly.
Can one couple's number be constantly engaged and another couple's free?
Like all the big shows, Strictly Come Dancing uses a voting system where at least the first eight digits of the phone numbers are the same for all contestants, with only the last few digits of the phone number changing depending on who you want to vote for.
As the telephone network only uses the first eight digits in a telephone number to route calls to the voting system, it is impossible for calls for different couples to be treated differently.
Once calls reach the voting system they are answered in turn, on a first-come, first-served basis. Each answering point is instructed to accept votes for all couples; there are no dedicated answering points for individual couples.
This means that your chance of getting through to vote will never depend on the celebrity or couple you wish to vote for.